Question 124
We are given a convex quadrilateral $A B C D$ whose angles are not right. Assume there are points $P, Q, R, S$ on its sides $A B, B C, C D, D A$, respectively, such that $P S \| B D$, $S Q \perp B C$, $P R \perp C D$. Furthermore, assume that the lines $P R, S Q$, and $A C$ are concurrent. Prove that the points $P, Q, R, S$ are concyclic.