Question 38
Given cyclic quadrilateral $ABCD$, let $L$ pass through circumcenter $O$, and let $P$ move on $L$. Circle $c_1$ passes through the feet from $P$ to $AB$, $BC$, $CA$; circle $c_2$ passes through the feet from $P$ to $AB$, $BD$, $DA$. Suppose circles $c_1, c_2$ intersect at $P_1, Q$, where $P_1$ is the foot from $P$ to $AB$. As $P$ moves on $L$, what is the locus of $Q$?