090321

Question: The incicrlce of ∆ABC touches the sides BC, CA and AB at D, E and F respectively. If AB=AC, prove that BD=CD.

Doubt by Sanya

Solution : 

Proof : We know, the length of tangents drawn from an external point to a circle are equal.

AF = AE — (1)

BF = BD — (2)

CE = CD — (3)

AB = AC (Given)

AF+BF = AE + CE 

AF+BF = AF + CE [From eq (1)]

BF = CE

BD = CD [From eq (2) and (3)]

Hence Proved.