Question 60
In $\triangle ABC$, $\angle B \gt \angle C$. Let $D$ be the point on side $BC$ such that $\angle DAC = \frac{B-C}{2}$. The circumcircle of $\triangle ACD$ meets side $AB$ again at $E$. The circumcircle of $\triangle ABD$ meets side $AC$ again at $F$. The internal angle bisector of $\angle BDE$ meets side $AB$ at $P$. The internal angle bisector of $\angle CDF$ meets side $AC$ at $Q$. Prove that $PQ$ and $AB$ are perpendicular.