A circle is touching the side BC of tri. ABC at P and touching AB and AC produced at Q and R respectively. Prove that AQ= 1/2 (perimeter of trip.ABC)

Asked by anujha.anujha | 16th Mar, 2015, 01:39: PM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
A s space t h e space tan g e n t s space f r o m space a n space e x t e r n a l space p o i n t space t o space t h e space c i r c l e space a r e space e q u a l comma space w e space h a v e comma space B Q equals B P space a n d space C P equals C R N o w space c o n s i d e r space t h e space p e r i m e t e r space o f space t h e space t r i a n g l e space A B C equals A B plus B C plus C A equals A B plus B P plus C P plus C A equals A B plus B Q plus C R plus C A equals A Q plus A R equals 2 A Q rightwards double arrow A Q equals 1 half cross times P e r i m e t e r space o f space t h e space t r i a n g l e space A B C

Answered by Vimala Ramamurthy | 17th Mar, 2015, 09:07: AM

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