{"id":5226,"date":"2022-10-21T11:00:21","date_gmt":"2022-10-21T11:00:21","guid":{"rendered":"https:\/\/www.studyzonebd.com\/math\/?p=5226"},"modified":"2022-10-21T11:28:14","modified_gmt":"2022-10-21T11:28:14","slug":"class-8-chapter-9-lesson-9","status":"publish","type":"post","link":"https:\/\/www.studyzonebd.com\/math\/class-8-chapter-9-lesson-9\/","title":{"rendered":"\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf"},"content":{"rendered":"\n

\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math <\/a>Book Solution | Chapter <\/a>09 : Pythagorean theorem| Class 8 math book Online Solution in Bangla (BD)<\/p>\n\n\n\n

\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef : \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af – PDF<\/a><\/h4>\n\n\n\n

\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u0989\u09a4\u09cd\u09a4\u09b0 \u098f\u0996\u09be\u09a8\u09c7 \u09b0\u09df\u09c7\u099b\u09c7\u0964 \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/p>\n\n\n\n

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\u0995) 800     <\/sup>\u0996) 900    <\/sup> \u0997) 1000    <\/sup> \u0998) 1200<\/sup><\/p>\n\n\n\n

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\u0995) 400      <\/sup>\u0996) 42.50      <\/sup>\u0997) 47.50       <\/sup>\u0998) 500<\/sup><\/p>\n\n\n\n

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\u0995) 4, 4, 5    \u0996) 5, 12, 13<\/p>\n\n\n\n

\u0997) 8, 10, 12    \u0998) 2, 3, 4<\/p>\n\n\n\n

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i. \u0985\u09a4\u09bf\u09ad\u09c1\u099c BC<\/p>\n\n\n\n

ii. \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2=\u00bd.AB.AC<\/p>\n\n\n\n

iii. BC2<\/sup>=AB2<\/sup>+AC2<\/sup><\/p>\n\n\n\n

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ii. \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09a4\u09b0 \u09ac\u09be\u09b9\u09c1\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09ac\u09c3\u09b9\u09a4\u09cd\u09a4\u09ae \u09ac\u09be\u09b9\u09c1\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/p>\n\n\n\n

iii. \u09b8\u09c2\u0995\u09cd\u09b7\u09cd\u09ae\u0995\u09cb\u09a3\u09a6\u09cd\u09ac\u09af\u09bc \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09aa\u09c2\u09b0\u0995<\/p>\n\n\n\n

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\u0995) I \u0993 ii     \u0996) I \u0993 iii    \u0997) ii \u0993 iii   \u0998) i, ii \u0993 iii<\/p>\n\n\n\n

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\"\"<\/figure>\n\n\n\n

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\u0995) 6    \u0996) 6.5    \u0997) 7     \u0998) 9.5<\/p>\n\n\n\n

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\u0995) 39    \u0996) 32.5    \u0997) 30    \u0998) 15<\/p>\n\n\n\n

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\u0995) 15    \u0996) 12.5    \u0997) 10    \u0998) 7.5<\/p>\n\n\n\n

\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

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\"\"<\/figure>\n\n\n\n

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\u0995) 64     \u0996) 96    \u0997) 100    \u0998) 144<\/p>\n\n\n\n

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\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

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\u0995) 46 \u09ac\u09b0\u09cd\u0997 \u09ae\u09bf\u09ae\u09bf    \u0996) 48 \u09ac\u09b0\u09cd\u0997 \u09ae\u09bf\u09ae\u09bf    \u0997) 50 \u09ac\u09b0\u09cd\u0997 \u09ae\u09bf\u09ae\u09bf   \u0998) 52 \u09ac\u09b0\u09cd\u0997 \u09ae\u09bf\u09ae\u09bf<\/p>\n\n\n\n

\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

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\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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ABC \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09ac\u09be\u09b9\u09c1 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c<\/p>\n\n\n\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, AB=BC=CA\u2026\u2026(i)<\/p>\n\n\n\n

AD, BC \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac<\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7, BD=DC, \u09ac\u09be, BD=DC= \u00bdBC [\u09b8\u09ae\u09ac\u09be\u09b9\u09c1 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09ac\u09be\u09b9\u09c1\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b2\u09ae\u09cd\u09ac \u09ad\u09c2\u09ae\u09bf\u0995\u09c7 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a8\u09cd\u09a1\u09bf\u09a4 \u0995\u09b0\u09c7]<\/p>\n\n\n\n

\u09b6\u09b0\u09cd\u09a4\u09ae\u09a4\u09c7, \u25b3ABD \u0993 \u25b3ADC \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u0964<\/p>\n\n\n\n

\u2234 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u25b3ABD \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>=AD2<\/sup>+BD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>-BD2<\/sup>=AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>– (\u00bdBC)2<\/sup>=AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>– \u00bcBC2<\/sup>=AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be,  BC2<\/sup>– \u00bcBC2<\/sup>=AD2<\/sup> [(i) \u09a8\u0982 \u09b9\u09a4\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

       4BC2<\/sup>-BC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, ————- = AD2<\/sup><\/p>\n\n\n\n

           4<\/p>\n\n\n\n

\u09ac\u09be, 4BC2<\/sup>-BC2<\/sup>=4AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, 3BC2<\/sup>=4AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>+BC2<\/sup>+CA2<\/sup>=4AD2  <\/sup>[(i) \u09a8\u0982 \u09b9\u09a4\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

\u2234 AB2<\/sup>+BC2<\/sup>+CA2<\/sup>=4AD2<\/sup> (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09eb. ABCD \u099a\u09a4\u09c1\u09b0\u09cd\u09ad\u09c1\u099c\u09c7\u09b0 \u0995\u09b0\u09cd\u09a3 \u09a6\u09c1\u0987\u099f\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u0995\u09c7 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, AB2<\/sup>+CD2<\/sup>=BC2<\/sup>+AD2<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, ABCD \u099a\u09a4\u09c1\u09b0\u09cd\u09ad\u09c1\u099c\u09c7\u09b0 \u09a6\u09c1\u0987\u099f\u09bf \u0995\u09b0\u09cd\u09a3 AC \u0993 BD \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 O \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u0964\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, AB2<\/sup>+CD2<\/sup>=BC2<\/sup>+AD2<\/sup>.<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

AC \u0993 BD \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 O \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6<\/p>\n\n\n\n

\u0985\u09a4\u098f\u09ac, \u2220AOB=\u2220BOC=\u2220COD=\u2220AOD=900<\/sup><\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7, \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u25b3AOB \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>=AO2<\/sup>+BO2<\/sup>\u2026\u2026\u2026\u2026.(i)<\/p>\n\n\n\n

\u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

CD2<\/sup>=DO2<\/sup>+CO2<\/sup>\u2026\u2026\u2026\u2026.(ii)<\/p>\n\n\n\n

AD2<\/sup>= AO2<\/sup>+DO2<\/sup>\u2026\u2026\u2026\u2026(iii)<\/p>\n\n\n\n

BC2<\/sup>= BO2<\/sup>+CO2<\/sup>\u2026\u2026\u2026\u2026(iv)<\/p>\n\n\n\n

(i)+(ii) \u0995\u09b0\u09c7,<\/p>\n\n\n\n

AB2<\/sup>+CD2<\/sup>=AO2<\/sup>+BO2<\/sup>+DO2<\/sup>+CO2<\/sup><\/p>\n\n\n\n

            =(AO2<\/sup>+DO2<\/sup>)+(BO2<\/sup>+CO2<\/sup>)<\/p>\n\n\n\n

            =AD2<\/sup>+BC2<\/sup> [(iii) \u0993 (iv) \u09b9\u09a4\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

\u2234 AB2<\/sup>+CD2<\/sup>=BC2<\/sup>+AD2 <\/sup>(\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09ec. ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0\u00a0\u2220A \u09b8\u09ae\u0995\u09cb\u09a3 \u098f\u09ac\u0982 CD \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ae\u09be\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, BC2<\/sup>=CD2<\/sup>+3AD2<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u2220A=\u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3 \u098f\u09ac\u0982 CD \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ae\u09be\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, BC2<\/sup>=CD2<\/sup>+3AD2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u2220A=\u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3<\/p>\n\n\n\n

\u25b3 ABC-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

BC2<\/sup>=AC2<\/sup>+AB2<\/sup>\u2026\u2026\u2026(i)<\/p>\n\n\n\n

\u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7, \u25b3ADC-\u098f<\/p>\n\n\n\n

CD2<\/sup>=AD2<\/sup>+AC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AC2<\/sup>=CD2<\/sup>-AD2<\/sup>\u2026\u2026\u2026(ii)<\/p>\n\n\n\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09ac\u09be\u09b9\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b0\u09c7\u0996\u09be\u0982\u09b6 \u09ae\u09a7\u09cd\u09af\u09ae\u09be\u0964<\/p>\n\n\n\n

\u09b8\u09c7\u09b9\u09c7\u09a4\u09c1 AD=BD, \u09ac\u09be, AD=\u00bdAB, \u09ac\u09be, AB=2AD\u2026\u2026(iii)<\/p>\n\n\n\n

\u098f\u0996\u09a8, (iii) \u0993 (ii) \u09b9\u09a4\u09c7 \u09ae\u09be\u09a8 (i) \u09a8\u0982 \u098f \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,           <\/p>\n\n\n\n

BC2<\/sup>=CD2<\/sup>-AD2<\/sup>+(2AD)2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, BC2<\/sup> =CD2<\/sup>-AD2<\/sup>+4AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, BC2<\/sup> =CD2<\/sup>+3AD2<\/sup> (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09ed. ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0\u00a0\u2220A \u09b8\u09ae\u0995\u09cb\u09a3 BP \u0993 CQ \u09a6\u09c1\u0987\u099f\u09bf \u09ae\u09a7\u09cd\u09af\u09ae\u09be\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, 5BC2<\/sup>=4(BP2<\/sup>+CQ2<\/sup>)<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u2220A \u09b8\u09ae\u0995\u09cb\u09a3 BP \u0993 CQ \u09a6\u09c1\u0987\u099f\u09bf \u09ae\u09a7\u09cd\u09af\u09ae\u09be\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, 5BC2<\/sup>=4(BP2<\/sup>+CQ2<\/sup>)<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u25b3ABC \u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

BC2<\/sup>=AB2<\/sup>+AC2<\/sup>\u2026\u2026..(i)<\/p>\n\n\n\n

\u25b3ABP-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

BP2<\/sup>=AB2<\/sup>+AP2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, BP2<\/sup>=AB2<\/sup>+ (\u00bdAC)2<\/sup> [BP \u09ae\u09a7\u09cd\u09af\u09ae\u09be \u09ac\u09b2\u09c7]<\/p>\n\n\n\n

\u09ac\u09be, BP2<\/sup>=AB2<\/sup>+ \u00bcAC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, 4BP2<\/sup>=4AB2<\/sup>+AC2<\/sup> [\u0989\u09ad\u09af\u09bc\u09aa\u0995\u09cd\u09b7\u0995\u09c7 4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0997\u09c1\u09a3 \u0995\u09b0\u09c7]\u2026\u2026\u2026.(ii)    <\/p>\n\n\n\n

\u25b3 ACQ-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

CQ2<\/sup>=AC2<\/sup>+AQ2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, CQ2<\/sup>=AC2<\/sup>+ (\u00bdAB)2<\/sup> [CQ \u09ae\u09a7\u09cd\u09af\u09ae\u09be \u09ac\u09b2\u09c7]<\/p>\n\n\n\n

\u09ac\u09be, CQ2<\/sup>=AC2<\/sup>+ \u00bcAB2<\/sup><\/p>\n\n\n\n

\u09ac\u09be,  4CQ2<\/sup>=4AC2<\/sup>+AB2<\/sup>  [\u0989\u09ad\u09af\u09bc\u09aa\u0995\u09cd\u09b7\u0995\u09c7 4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0997\u09c1\u09a3 \u0995\u09b0\u09c7]\u2026\u2026\u2026.(iii)<\/p>\n\n\n\n

(ii)+(iii) \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

4BP2<\/sup>+4CQ2<\/sup>=4AB2<\/sup>+AC2<\/sup>+4AC2<\/sup>+AB2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, 4(BP2<\/sup>+CQ2<\/sup>)=5AB2<\/sup>+5AC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, 4(BP2<\/sup>+CQ2<\/sup>)=5(AB2<\/sup>+AC)2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, 4(BP2<\/sup>+CQ2<\/sup>)=5BC2<\/sup> [(i) \u09a8\u0982 \u09b9\u09a4\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

\u09ac\u09be, 5BC2<\/sup>=4(BP2<\/sup>+CQ2<\/sup>) [\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e7\u09ee. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, \u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u0990 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u09c7\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, ABCD \u098f\u0995\u099f\u09bf \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u0995\u09b0\u09cd\u09a3 AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7 AC \u098f\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 ABCD \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u09c7\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3\u0964<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

AC \u098f\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 = AC2<\/sup><\/p>\n\n\n\n

\u098f\u09ac\u0982 ABCD \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 = a2<\/sup>=AB2<\/sup>=BC2<\/sup>=CD2<\/sup>=AD2 <\/sup>[\u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995 \u09ac\u09be\u09b9\u09c1\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af a \u09a7\u09b0\u09c7]<\/p>\n\n\n\n

\u098f\u0996\u09a8, \u2220ADC=900 <\/sup>[\u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995 \u0995\u09cb\u09a3 \u09b8\u09ae\u0995\u09cb\u09a3]<\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7, \u25b3ADC-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AC2<\/sup>=AD2<\/sup>+DC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be,  AC2<\/sup>=a2<\/sup>+a2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AC2<\/sup>=2a2<\/sup><\/sup><\/p>\n\n\n\n

\u09ac\u09be, AC \u098f\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2=\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09ef. \u099a\u09bf\u09a4\u09cd\u09b0\u09c7 OB=4 \u09b8\u09c7\u09ae\u09bf \u09b9\u09b2\u09c7 BD \u098f\u09ac\u0982 AC \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09a7\u09b0\u09bf, BD=x<\/p>\n\n\n\n

\u2234 DO=4-x<\/p>\n\n\n\n

\u099a\u09bf\u09a4\u09cd\u09b0\u09c7, \u25b3CBD \u0993 \u25b3ADO-\u098f<\/p>\n\n\n\n

\u2220CBD=\u2220AOD=900<\/sup><\/p>\n\n\n\n

\u2220BDC=\u2220ADO [\u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09c0\u09aa \u0995\u09cb\u09a3]<\/p>\n\n\n\n

\u2234\u2220BCD=\u2220DAO<\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7, \u25b3CBD \u0993 \u25b3ADO \u09b8\u09a6\u09c3\u09b6\u0964<\/p>\n\n\n\n

\u0985\u09a4\u098f\u09ac,<\/p>\n\n\n\n

BC         BD<\/p>\n\n\n\n

—– = ——<\/p>\n\n\n\n

AO        DO<\/p>\n\n\n\n

\u09ac\u09be, BC.DO=AO.BD<\/p>\n\n\n\n

\u09ac\u09be, 5.(4-x)=3.x<\/p>\n\n\n\n

\u09ac\u09be, 20-5x=3x<\/p>\n\n\n\n

\u09ac\u09be, 20=3x+5x<\/p>\n\n\n\n

\u09ac\u09be, 8x=20<\/p>\n\n\n\n

\u09ac\u09be, x= 20\/8<\/p>\n\n\n\n

\u09ac\u09be, x= 5\/2<\/p>\n\n\n\n

\u09ac\u09be, BD=2.5 cm<\/p>\n\n\n\n

\u2234 DO=4-2.5=1.5 cm<\/p>\n\n\n\n

\u25b3CBD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

CD2<\/sup>=CB2<\/sup>+BD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, CD2<\/sup> =52<\/sup>+(2.5)2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, CD2<\/sup> =25+6.25<\/p>\n\n\n\n

\u09ac\u09be, CD2<\/sup>=31.25<\/p>\n\n\n\n

\u09ac\u09be, CD=5.590<\/p>\n\n\n\n

\u25b3ADO -\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AD2<\/sup>=AO2<\/sup>+DO2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AD2<\/sup>=32<\/sup>+(1.5)2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AD2<\/sup>=9+2.25<\/p>\n\n\n\n

\u09ac\u09be, AD2<\/sup>=11.25<\/p>\n\n\n\n

\u09ac\u09be, AD=3.35<\/p>\n\n\n\n

\u2234 CD+AD=5.590+3.354=8.944<\/p>\n\n\n\n

\u09ac\u09be, AC=8.944 cm<\/p>\n\n\n\n

 \u2234 BD=2.5 cm<\/p>\n\n\n\n

AC=8.944 cm<\/p>\n\n\n\n

\u09e8\u09e6. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, \u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u098f\u09b0 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0985\u09b0\u09cd\u09a7\u09c7\u0995\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, ABCD \u098f\u0995\u099f\u09bf \u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u0964 \u098f\u09b0 \u098f\u0995\u099f\u09bf \u0995\u09b0\u09cd\u09a3 AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, AB2<\/sup>=\u00bdAC2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u25b3ABC-\u098f \u2220B=\u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3 [\u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u0995\u09b2 \u0995\u09cb\u09a3 \u09b8\u09ae\u0995\u09cb\u09a3]<\/p>\n\n\n\n

\u2234 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AC2<\/sup>=AB2<\/sup>+BC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AC2<\/sup>=AB2<\/sup>+AB2<\/sup> [\u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u0995\u09b2 \u09ac\u09be\u09b9\u09c1 \u09b8\u09ae\u09be\u09a8]<\/p>\n\n\n\n

\u09ac\u09be, AC2<\/sup>=2AB2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>= \u00bdAC2 <\/sup>[\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e8\u09e7. ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0\u00a0\u2220A= \u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u0964\u00a0\u00a0D, AC \u098f\u09b0 \u0989\u09aa\u09b0\u09b8\u09cd\u09a5 \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, BC2<\/sup>+AD2<\/sup>=BD2<\/sup>+AC2.<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u2220A= \u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u0964  D, AC \u098f\u09b0 \u0989\u09aa\u09b0\u09b8\u09cd\u09a5 \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, BC2<\/sup>+AD2<\/sup>=BD2<\/sup>+AC2.<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u25b3ABC -\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

BC2<\/sup>=AB2<\/sup>+AC2<\/sup><\/p>\n\n\n\n

\u25b3ADB -\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>+AD2<\/sup>=BD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AD2<\/sup>=BD2<\/sup>-AB2<\/sup><\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7,<\/p>\n\n\n\n

BC2<\/sup>+AD2<\/sup>= AB2<\/sup>+AC2<\/sup>+ BD2<\/sup>-AB2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, BC2<\/sup>+AD2<\/sup>=BD2<\/sup>+AC2<\/sup> [\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e8\u09e8. ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0\u00a0\u2220A= \u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u00a0\u00a0D \u0993 E \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 AB \u0993 AC \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09b2\u09c7, \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, DE2<\/sup>=CE2<\/sup>+BD2<\/sup>.<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u2220A= \u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3  D \u0993 E \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 AB \u0993 AC \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, DE2<\/sup>=CE2<\/sup>+BD2<\/sup>.<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u098f\u0996\u09be\u09a8\u09c7, AD=BD \u098f\u09ac\u0982 AE=CE [D \u0993 E \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 AB \u0993 AC \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1]<\/p>\n\n\n\n

\u25b3ADE-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

DE2<\/sup>=AE2<\/sup>+AD2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, DE2<\/sup>=CE2<\/sup>+BD2 <\/sup>[\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e8\u09e9.\u00a0\u25b3ABC \u098f BC \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac AD \u098f\u09ac\u0982 AB>AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, AB2<\/sup>-AC2<\/sup>=BD2<\/sup>-CD2<\/sup>.<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, \u25b3ABC \u098f BC \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac AD \u098f\u09ac\u0982 AB>AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, AB2<\/sup>-AC2<\/sup>=BD2<\/sup>-CD2<\/sup>.<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u25b3ABC \u098f BC \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac AD<\/p>\n\n\n\n

\u2234\u25b3ABD \u0993 \u25b3ADC \u0989\u09ad\u09af\u09bc\u0987 \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u0964<\/p>\n\n\n\n

\u25b3ABD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>=BD2<\/sup>+AD2<\/sup>\u2026\u2026.(i)<\/p>\n\n\n\n

\u25b3ADC-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AC2<\/sup>=AD2<\/sup>+DC2<\/sup>\u2026\u2026(ii)<\/p>\n\n\n\n

(i)-(ii) \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>-AC2<\/sup>= BD2<\/sup>+AD2<\/sup>-(AD2<\/sup>+DC2<\/sup>)<\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>-AC2<\/sup>= BD2<\/sup>+AD2<\/sup>-AD2<\/sup>-DC2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, AB2<\/sup>-AC2<\/sup>= BD2<\/sup>-DC2 <\/sup>[\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e8\u09ea.\u00a0\u25b3ABC \u098f BC \u098f\u09b0 \u0989\u09aa\u09b0 AD \u09b2\u09ae\u09cd\u09ac \u098f\u09ac\u0982 AD \u098f\u09b0 \u0989\u09aa\u09b0 P \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993\u00a0\u00a0AB>AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, PB2<\/sup>-PC2<\/sup>=AB2<\/sup>-AC2<\/sup>.<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, \u25b3ABC \u098f BC \u098f\u09b0 \u0989\u09aa\u09b0 AD \u09b2\u09ae\u09cd\u09ac \u098f\u09ac\u0982 AD \u098f\u09b0 \u0989\u09aa\u09b0 P \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993  AB>AC. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, PB2<\/sup>-PC2<\/sup>=AB2<\/sup>-AC2<\/sup>.<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 AD\u22a5BC \u09b8\u09c7\u09b9\u09c7\u09a4\u09c1 \u25b3ABD, \u25b3ACD, \u25b3BPD, \u25b3CPD \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u09c7\u0987 \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u0964<\/p>\n\n\n\n

\u25b3ABD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AB2<\/sup>=BD2<\/sup>+AD2<\/sup><\/p>\n\n\n\n

\u25b3ACD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

AC2<\/sup>=AD2<\/sup>+CD2<\/sup><\/p>\n\n\n\n

\u2234 AB2<\/sup>-AC2<\/sup>= BD2<\/sup>+AD2<\/sup>– AD2<\/sup>-CD2<\/sup>=BD2<\/sup>-CD2<\/sup>\u2026\u2026(i)<\/p>\n\n\n\n

\u25b3BPD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

PB2<\/sup>=PD2<\/sup>+BD2<\/sup><\/p>\n\n\n\n

\u25b3PCD-\u098f \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

PC2<\/sup>=PD2<\/sup>+CD2<\/sup><\/p>\n\n\n\n

PB2<\/sup>-PC2<\/sup>= PD2<\/sup>+BD2<\/sup>– PD2<\/sup>-CD2<\/sup>=BD2<\/sup>-CD2<\/sup>\u2026\u2026(ii)<\/p>\n\n\n\n

(i) \u0993 (ii) \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

PB2<\/sup>-PC2<\/sup>=AB2<\/sup>-AC2\u00a0<\/sup>[\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09e8\u09eb.<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u0995. PQST \u0995\u09c0 \u09a7\u09b0\u09a8\u09c7\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09ad\u09c1\u099c? \u09b8\u09cd\u09ac\u09aa\u0995\u09cd\u09b7\u09c7 \u09af\u09c1\u0995\u09cd\u09a4\u09bf \u09a6\u09be\u0993\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

PQST \u099a\u09a4\u09c1\u09b0\u09cd\u09ad\u09c1\u099c\u099f\u09bf \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09af\u09bc\u09be\u09ae\u0964 \u0995\u09be\u09b0\u09a3 PQST \u099a\u09a4\u09c1\u09b0\u09cd\u09ad\u09c1\u099c\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09ac\u09be\u09b9\u09c1 PQ \u0993 TS \u09ac\u09be\u09b9\u09c1\u09a6\u09cd\u09ac\u09af\u09bc \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09ac\u0982 \u0985\u09aa\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 PT \u0993 QS \u09ac\u09be\u09b9\u09c1\u09a6\u09cd\u09ac\u09af\u09bc \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u0964<\/p>\n\n\n\n

\u0996. \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, <\/strong>\u25b3<\/strong>PRT \u09b8\u09ae\u0995\u09cb\u09a3\u09c0\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u25b3PQR \u0993 \u25b3RST \u098f<\/p>\n\n\n\n

PQ=RS=b, QR=ST=a \u098f\u09ac\u0982 \u2220PQR=\u2220RST=900<\/sup><\/p>\n\n\n\n

\u2234 \u25b3PQR\u2245\u25b3RST<\/p>\n\n\n\n

\u09a4\u09be\u09b9\u09b2\u09c7, PR=RT=c \u098f\u09ac\u0982 \u2220QPR=\u2220TRS.<\/p>\n\n\n\n

\u0986\u09ac\u09be\u09b0, PC\u22a5QS \u098f\u09ac\u0982 TS\u22a5QS \u09ac\u09b2\u09c7, PQ\u0964\u0964TS.<\/p>\n\n\n\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, PQST \u098f\u0995\u099f\u09bf \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09af\u09bc\u09be\u09ae\u0964<\/p>\n\n\n\n

\u098f\u0996\u09a8, \u2220PRQ+\u2220QPR=\u2220RTS+\u2220TRS=\u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u0964<\/p>\n\n\n\n

\u2234 \u2220PRT=\u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u25b3PRT \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u0964  <\/p>\n\n\n\n

\u0997. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 PR2<\/sup>=PQ2<\/sup>+QR2<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

PQST \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09af\u09bc\u09be\u09ae \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2= \u25b3PQR \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0+\u25b3RST \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0+\u25b3PRT \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0<\/p>\n\n\n\n

\u09ac\u09be, \u00bdQS(PQ+TS)=\u00bd.ab+\u00bd.ab+\u00bdc2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, \u00bd.(QR+RS)(PQ+TS)=\u00bd(2ab+c2<\/sup>)<\/p>\n\n\n\n

\u09ac\u09be, \u00bd.(a+b)(b+a)= \u00bd(2ab+c2<\/sup>)<\/p>\n\n\n\n

\u09ac\u09be, a2<\/sup>+2ab+b2<\/sup>=2ab+c2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, a2<\/sup>+b2<\/sup>=c2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, c2<\/sup>=b2<\/sup>+a2\u09aa<\/sup><\/p>\n\n\n\n

\u2234 PR2<\/sup>=PQ2<\/sup>+QR2<\/sup> (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)        <\/p>\n\n\n\n

\u09e8\u09ec.\u00a0\u25b3PQR \u098f\u00a0\u2220P=900<\/sup>, PQ \u098f\u09ac\u0982 PR \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 M \u0993 N\u0964<\/strong><\/p>\n\n\n\n

\u0995. \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u099f\u09bf \u0986\u0981\u0995\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 \u09a8\u09bf\u09a8\u09cd\u09ae\u09b0\u09c2\u09aa\u0983<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u0996. \u099a\u09bf\u09a4\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, PR2<\/sup>+PQ2<\/sup>=QR2<\/sup>.<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, PQR \u098f \u2220P=900<\/sup>\u0964 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, PR2<\/sup>+PQ2<\/sup>=QR2<\/sup>.<\/p>\n\n\n\n

\u0985\u0999\u09cd\u0995\u09a8\u0983<\/strong><\/p>\n\n\n\n

PQ \u0995\u09c7 S \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 \u0995\u09b0\u09bf \u09af\u09c7\u09a8 QS=PR \u09b9\u09af\u09bc \u098f\u09ac\u0982 S \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 ST  \u09b2\u09ae\u09cd\u09ac \u0986\u0981\u0995\u09bf \u09af\u09c7\u09a8 ST=PQ \u09b9\u09af\u09bc\u0964 Q, T; T, R \u09af\u09cb\u0997 \u0995\u09b0\u09bf\u0964<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0983<\/strong><\/p>\n\n\n\n

\u25b3PQR \u0993 \u25b3QST \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7,<\/p>\n\n\n\n

PQ=ST; PR=QS<\/p>\n\n\n\n

\u2220RPS=\u2220QST=900<\/sup><\/p>\n\n\n\n

\u25b3PQR \u2245 \u25b3QST<\/p>\n\n\n\n

\u2234 RS=QT \u098f\u09ac\u0982 \u2220PRS=\u2220TQS.<\/p>\n\n\n\n

\u0985\u09a4\u098f\u09ac, \u2220PRQ+\u2220RQP=\u2220SQT+\u2220QTS=900<\/sup><\/p>\n\n\n\n

\u2234 RQT=900<\/sup><\/p>\n\n\n\n

\u0985\u09a4\u098f\u09ac, \u25b3RQT \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u0964<\/p>\n\n\n\n

\u098f\u0996\u09a8, RP\u22a5PS \u0993 TS\u22a5PS; \u09a4\u09be\u09b9\u09b2\u09c7 RS\u0964\u0964TS.<\/p>\n\n\n\n

\u2234 PSTR \u098f\u0995\u099f\u09bf \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09af\u09bc\u09be\u09ae\u0964<\/p>\n\n\n\n

PSTR \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09af\u09bc\u09be\u09ae \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2=\u25b3PQR \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2+\u25b3QST \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2+\u25b3RQT \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/p>\n\n\n\n

\u09ac\u09be, \u00bdPS(PR+ST)= \u00bd.PR.PQ+ \u00bd.QS.ST+ \u00bd.RQ.QT<\/p>\n\n\n\n

\u09ac\u09be, \u00bd.(PQ+QS)(PR+ST)= \u00bd.PR.PQ+ \u00bd.PR.PQ+ \u00bd.RQ.RQ [\u09b8\u09b0\u09cd\u09ac\u09b8\u09ae\u09a4\u09be \u09a5\u09c7\u0995\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09a4\u09a5\u09cd\u09af \u09b9\u09a4\u09c7]<\/p>\n\n\n\n

\u09ac\u09be, \u00bd.(PQ+PR)(PR+PQ)= \u00bd.PR.PQ+ \u00bd.PR.PQ+ \u00bd.RQ2<\/sup>  [\u09b8\u09b0\u09cd\u09ac\u09b8\u09ae\u09a4\u09be \u09a5\u09c7\u0995\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09a4\u09a5\u09cd\u09af \u09b9\u09a4\u09c7]<\/p>\n\n\n\n

\u09ac\u09be, (PQ+PR)2<\/sup>=PR.PQ+PR.PQ+RQ2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, (PQ+PR)2<\/sup>=2.PR.PQ+RQ2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, PQ2<\/sup>+PR2<\/sup>+2.PR.PQ =2.PR.PQ+RQ2<\/sup><\/p>\n\n\n\n

\u09ac\u09be, PQ2<\/sup>+PR2<\/sup>=RQ2 <\/sup>[\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u0997. \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 5RQ2<\/sup>=4(RM2<\/sup>+NQ2<\/sup>)<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a8\u09bf\u09b0\u09cd\u09ac\u099a\u09a8\u0983<\/strong><\/p>\n\n\n\n

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\u09ac\u09be, RM2<\/sup>=PR2<\/sup>+ \u00bcPQ2<\/sup><\/strong><\/p>\n\n\n\n

\u09ac\u09be, 4RM2<\/sup>=4PR2<\/sup>+PQ2<\/sup> [\u0989\u09ad\u09af\u09bc\u09aa\u0995\u09cd\u09b7\u0995\u09c7 4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0997\u09c1\u09a3 \u0995\u09b0\u09c7]\u2026\u2026\u2026.(ii)    <\/strong><\/p>\n\n\n\n

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\u09ac\u09be, 5RQ2<\/sup>=4(RM2<\/sup>+NQ2<\/sup>) [\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\n\n\n\n
Class 8 math book all chapter solution Bangla version pdf | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 PDF<\/td><\/tr>
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tags: <\/em>Bangladesh, Bangla, Bengali, Class 8\/jsc math solution 2021 pdf, 8th class maths guide pdf free download, math book solution BD, JSC srijonshil math, Chapter 9, \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math Book Solution | Chapter 09 : Pythagorean theorem| Class 8 math book Online Solution in Bangla (BD) \u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef : \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af – PDF \u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 […]<\/p>\n","protected":false},"author":1,"featured_media":4919,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[36],"tags":[37,38],"class_list":["post-5226","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-eight-8","tag-class-8","tag-class-eight"],"yoast_head":"\n\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD<\/title>\n<meta name=\"description\" content=\"\u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math Book Solution. Chapter 09 : Pythagorean theorem. \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.studyzonebd.com\/math\/class-8-chapter-9-lesson-9\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u09ef\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09aa\u09bf\u09a5\u09be\u0997\u09cb\u09b0\u09be\u09b8\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ef | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD\" \/>\n<meta property=\"og:description\" content=\"\u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math Book Solution. 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