KöMaL 2022 B5267

We are given two line segments of length $p$ and $q$, and a triangle $ABC$ determined by the lines $a$, $b$ and $c$ (where the usual convention is used: points $B$ and $C$ lie on line $a$, and so on). Construct the point $P$ on the circumcircle of the triangle for which the point $P_a$ divides the line segment $P_bP_c$ in a ratio $p: q$, where $P_x$ is the orthogonal projection of the point $P$ onto the line $x$.