MathNet 2017-part-05 — 176 problems (EN–VI) Question 126

A circle centered at $I$ is inscribed into a quadrilateral $ABCD$. $BA$ and $CD$ meet at $P$, and rays $AD$ and $BC$ meet at $Q$. Given that $P$ lies on the circle $(AIC)$, prove that $Q$ also lies on this circle.