MathNet 2023-part-06 — 191 problems (EN–VI) Question 183

An acute-angled triangle is given $ABC$ with the circumcircle $\omega$. The points $F$ on $AC$, $E$ on $AB$ and $P, Q$ on $\omega$ are selected so that $\angle AFB = \angle AEC = \angle APE = \angle AQF = 90^\circ$. Prove that the lines $BC, EF$ and $PQ$ intersect at one point.


**Fig. 12**