UA-UMO 1999 Problem 94

The bisectors of angles $A,B,C$ of a triangle $ABC$ intersect the circumcircle of the triangle at $A_1,B_1,C_1$ , respectively. Let $P$ be the intersection of the lines $B_1C_1$ and $AB$ , and $Q$ be the intersection of the lines $B_1A_1$ and $BC$ . Show how to construct the triangle $ABC$ by a ruler and a compass, given its circumcircle, points $P$ and $Q$ , and the halfplane determined by $PQ$ in which point $B$ lies.