Question 30
Triangle $ABC$ is inscribed in a circle $\omega$ such that $\angle A = 60^\circ$ and $\angle B = 75^\circ$. Let the bisector of angle $A$ meet $BC$ and $\omega$ at $E$ and $D$, respectively. Let the reflections of $A$ across $D$ and $C$ be $D'$ and $C'$, respectively. If the tangent to $\omega$ at $A$ meets line $BC$ at $P$, and the circumcircle of $APD'$ meets line $AC$ at $F \neq A$, prove that the circumcircle of $C'FE$ is tangent to $BC$ at $E$.
