Question 20
(FRA 1) IMO4. In the plane, let there be given a circle $C$, a line $l$ tangent to $C$, and a point $M$ on $l$. Find the locus of points $P$ that have the following property: There exist two points $Q$ and $R$ on $l$ such that $M$ is the midpoint of $QR$ and $C$ is the incircle of $PQR$.