if a,b (b>a)be the diametres of 2 cocentric circles and c be a chord of acircle which is tangent to the other circle, prove that a2=c2+b2

Asked by richaverma914 | 6th Jan, 2016, 01:30: PM

Expert Answer:

T h e space t w o space c o n c e n t r i c space c i r c l e s space a r e space s h o w n space i n space t h e space f i g u r e. T h e space c h o r d space o f space t h e space b i g g e r space c i r c l e space i s space a space tan g e n t space t o space t h e space s m a l l e r space o n e. S o space i f space w e space d r a w space a space p e r p e n d i c u l a r space f r o m space c e n t r e space t o space t h e space c h o r d comma space w e space g e t space r a d i u s space o f space t h e space s m a l l e r space c i r c l e comma space w h i c h space i s space a divided by 2. T h i s space p e r p e n d i c u l a r space w i l l space b i s e c t space t h e space c h o r d. S o space w e space g e t space a space r i g h t space a n g l e d space t r i a n g l e space a s space s h o w n comma space w h o s e space h y p o t e n u s e space i s space b divided by 2. H e n c e comma space open parentheses b over 2 close parentheses squared equals open parentheses a over 2 close parentheses squared plus open parentheses c over 2 close parentheses squared b squared over 4 equals a squared over 4 plus c squared over 4 rightwards double arrow b squared equals a squared plus c squared  T h e space r e l a t i o n space y o u space h a v e space m e n t i o n e d space i n space t h e space q u e s t i o n space s e e m s space i n c o r r e c t. space P l e a s e space c h e c k.

Answered by satyajit samal | 7th Jan, 2016, 12:20: PM