Question 1
(PHI 3) Let $ABC$ be any triangle and $P$ any point in its interior. Let $P_1,P_2$ be the feet of the perpendiculars from $P$ to the two sides $AC$ and $BC$. Draw $AP$ and $BP$, and from $C$ drop perpendiculars to $AP$ and $BP$. Let $Q_1$ and $Q_2$ be the feet of these perpendiculars. Prove that the lines $Q_1P_2$, $Q_2P_1$, and $AB$ are concurrent.