Question 2
In triangle $ABC$ point $A_1$ lies on side $BC$ and point $B_1$ lies on side $AC$. Let $P$ and $Q$ be points on segments $AA_1$ and $BB_1$, respectively, such that $\overline{PQ} \parallel \overline{AB}$. Point $P_1$ is chosen on ray $PB_1$ beyond $B_1$ such that $\angle PP_1C = \angle BAC$. Point $Q_1$ is chosen on ray $QA_1$ beyond $A_1$ such that $\angle CQ_1Q = \angle CBA$. Prove that points $P_1$, $Q_1$, $P$, $Q$ are cyclic.