OMM 1998 Problem 2

Rays $l$ and $m$ forming an angle of $a$ are drawn from the same point. Let $P$ be a fixed point on $l$ . For each circle $C$ tangent to $l$ at $P$ and intersecting $m$ at $Q$ and $R$ , let $T$ be the intersection point of the bisector of angle $QPR$ with $C$ . Describe the locus of $T$ and justify your answer.