SHARYGIN 2009 Problem 103

The cirumradius and the inradius of triangle $ABC$ are equal to $R$ and $r, O, I$ are the centers of respective circles. External bisector of angle $C$ intersect $AB$ in point $P$ . Point $Q$ is the projection of $P$ to line $OI$ . Find distance $OQ.$ (A.Zaslavsky, A.Akopjan)