Question 15
Let $F$ be the point of tangency of the incircle of triangle $ABC$ with $AB$, and let $Z$ be an arbitrary point strictly between $B$ and $C$, as shown below. Let $K$ and $J$ be the points on the incircles of triangles $BFZ$ and $CAZ$, respectively, such that $KJ$ is the other exterior common tangent to these two circles. Prove that $KJ$ is also a tangent of the incircle of triangle $AFZ$.
