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A2चित्र में 40 । 80 तथा ह-1/800 है, तो सिद्ध कीजिए कि“2CA% =2AB? + BC? 21 |
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Answer» In right DADB, AB2= AD2+ BD2[By Pythagoras theorem] – (1)In right triangleADC, AC2= AD2+ CD2[By Pythagoras theorem] – (2)Subtract (1) from (2), we getAC2– AB2= AD2+ CD2– AD2– BD2AC2– AB2= CD2– BD2 --- (3)Given BD =1/3 CD From the figure, BD + DC = BC⇒ (1/3)CD + CD = BC⇒ (4/3)CD = BC∴ CD = 3BC/4⇒ BD = BC/4Equation (3) becomes,AC2– AB2= (3BC/4)2– (BC/4)2 = (8/16)BC2⇒ AC2– AB2= (1/2) BC2⇒ 2AC2– 2AB2= BC2⇒ 2AC2= 2AB2+ BC2 |
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