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Dear Pawan sir

Q.In a triangle ABC AD is perpendicular to BC and 4BD=CD. Prove that 5AB²=5AC²-3BC²

Can u plz answer this question for me

Regards

Tushar

Asked by panirudha2012 | 4th Sep, 2015, 09:58: PM

Expert Answer:

$G i v e n space t h a t space 4 B D equals C D. A D space i s space p e r p e n d i c u l a r space t o space B C. B y space a p p l y i n g space P y t h a g o r a s space T h e o r e m comma A B squared equals A D squared plus B D squared A D squared equals A B squared minus B D squared... left parenthesis 1 right parenthesis S i m i l a r l y comma space w e space h a v e comma A C squared equals A D squared plus C D squared rightwards double arrow A D squared equals A C squared minus C D squared... left parenthesis 2 right parenthesis B C equals B D plus C D rightwards double arrow B C squared equals open parentheses B D plus C D close parentheses squared rightwards double arrow B C squared equals B D squared plus C D squared plus 2 B D cross times C D rightwards double arrow B C squared equals B D squared plus 16 B D squared plus 2 B D cross times 4 B D space space space space space space open square brackets because 4 B D equals C D close square brackets rightwards double arrow B C squared equals B D squared plus 16 B D squared plus 8 B D squared rightwards double arrow B C squared equals 25 B D squared rightwards double arrow B D squared equals fraction numerator B C squared over denominator 25 end fraction... left parenthesis 3 right parenthesis E q u a t i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma A B squared minus B D squared equals A C squared minus C D squared rightwards double arrow A B squared minus A C squared equals B D squared minus C D squared rightwards double arrow A B squared minus A C squared equals B D squared minus 16 B D squared space space space space space space space space space space space space open square brackets because 4 B D equals C D comma space 16 B D squared space equals C D squared space close square brackets rightwards double arrow A B squared minus A C squared equals negative 15 B D squared space rightwards double arrow A B squared minus A C squared equals negative 15 cross times fraction numerator B C squared over denominator 25 end fraction space space space space space space space space open square brackets because B D squared equals fraction numerator B C squared over denominator 25 end fraction close square brackets space space space space rightwards double arrow A B squared minus A C squared equals negative fraction numerator 3 B C squared over denominator 5 end fraction space rightwards double arrow 5 A B squared minus 5 A C squared equals negative 3 B C squared space rightwards double arrow 5 A B squared equals 5 A C squared minus 3 B C squared space$

Answered by Vimala Ramamurthy | 5th Sep, 2015, 05:00: PM

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