KöMaL 2026 B5541

Let $A$, $B$ and $C$ be three points of a parabola with focus $F$, in this order. Let the tangent of the parabola at $B$ intersect the tangent at $P$ in point $A$, and the tangent at $C$ at point $Q$. Prove that the point of intersection of circles $FAP$ and $FCQ$ different from $F$ is on line $AC$.