Question

The incircle of a triange ABC touches the sides BC, CA and AB at D, E and F respectively. If AB = AC, prove that BD=CD.

Answer 1

GIVEN AB=AC......(1)

BY thm AF =AE (tangents from an external point to a circle are equal )...(2)

similarly BF =BD...(3)

and CD =CE...(4)

AB=AC

therefore AF +BF =AE +CE

from (2) AF =AE

THERE FORE BF =CE

but BF =BD (3) and CE =CD (4)

THEREFORE ....BD=CD