QUE
begin mathsize 26px style increment A B C space i s space a space r i g h t space a n g l e d space a t space B. D space i s space t h e space m i d p o i n t space o n space B C. p r o v e space t h a t A C squared equals 4 A D squared minus 3 A B squared end style

Asked by GURSHARNSUITS | 22nd Aug, 2015, 09:02: PM

Expert Answer:

C o n s i d e r space t h e space r i g h t space t r i a n g l e space r i g h t space a n g l e d space a t space B. G i v e n space t h a t space D space i s space t h e space m i d p o i n t space o f space B C.
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 space i n space triangle A B C comma space w e space h a v e comma A C squared equals A B squared plus B C squared... left parenthesis 1 right parenthesis S i n c e space D space i s space t h e space m i d p o i n t space o f space B C comma space w e space h a v e comma space B D equals C D T h u s comma space B C equals 2 B D rightwards double arrow B C squared equals 4 B D squared... left parenthesis 2 right parenthesis A g a i n space i n space r i g h t space t r i a n g l e space A B D comma space w e space h a v e comma A D squared equals A B squared plus B D squared rightwards double arrow B D squared equals A D squared minus A B squared... left parenthesis 3 right parenthesis U sin g space E q u a t i o n s space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma A C squared equals A B squared plus B C squared space space space space space space space space equals A B squared plus 4 B D squared space space space space space space space space equals A B squared plus 4 open parentheses A D squared minus A B squared close parentheses space space space space space space space space equals A B squared plus 4 A D squared minus 4 A B squared space space space space space space space space space equals 4 A D squared minus 3 A B squared space space space space space space space space space space

Answered by Vimala Ramamurthy | 23rd Aug, 2015, 10:00: AM

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