Question 135
In triangle $ABC$, we have $AB \gt AC$. The incircle $\omega$ touches $BC$ at $E$, and $AE$ intersects $\omega$ at $D$. Choose a point $F$ on $AE$ ($F$ is different from $E$), such that $CE = CF$. Let $G$ be the intersection point of $CF$ and $BD$. Prove that $CF = FG$.