Question
The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.
Solution
Given: is an isosceles triangle with a circle inscribed in the triangle.
To prove: BD=DC
Proof:
AF and AE are tangents drawn to the circle from point A.
Since two tangents drwan to a circle from the same exterior point are equal.
AF=AE=a
Similarly BF=BD=b and CD=CE=c
We also know that is an isosceles triangle
Thus AB=AC
a+b=a+c
Thus b=c
Therefore, BD=DC
Hence proved.
