IT-CESENATICO 1990 Problem 2

In a triangle $ABC$ , the bisectors of the angles at $B$ and $A$ meet the opposite sides at $P$ and $Q$ , respectively. Suppose that the circumcircle of triangle $PQC$ passes through the incenter $R$ of $\vartriangle ABC$ . Given that $PQ = l$ , find all sides of triangle $PQR$ .