KöMaL 2007 A416

In a right triangle ABC , point $F$ is the perpendicular foot of $C$ on hypotenuse $AB$. Let point $Q$ on $AB$ be the perpendicular foot of a certain point $P$ on leg $AC$. The line through $B$ which is perpendicular to $BP$ intersects line $CF$ at point $R$. Show that the intersection of circles with diameters $AC$ and $FQ$, different from $F$, lies in the interior of segment $PR$.