Question 79
Let $P,Q$ be interior points of triangle $ABC$ such that $\angle BAP=\angle CAQ$, $\angle ACP=\angle BCQ$ and $\angle CBP=\angle ABQ$. Reflect $Q$ in $BC,CA,AB$ to obtain $Q_1,Q_2,Q_3$, respectively. Set $D=PQ_1\cap BC$, $E=PQ_2\cap CA$, $F=PQ_3\cap AB$. Prove that $AD,BE,CF$ are concurrent.
