TITLE: Length of tangents of incircle and excircle
QUESTION [5 upvotes]: Given a triangle $ABC$ , the incircle touches side $BC $ at $D $ and the excircle touches the side $BC$ at $F$ .
Prove that $BF=CD$ .
Can't think of a way to relate the tangents of the incircle and the excircle.
Any tips please?

REPLY [3 votes]: I will provide a sketch of the proof: 

Let $a,b,c$ be the lengths of sides $BC,CA,AB$, respectively, and let $s=\frac{a+b+c}{2}$ be the semi-perimeter of the triangle.
Show that $CD=s-c$.
Show by similar logic that $BF=s-c$ as well.