Two Triangles Centers At Play

Geometry Level 1

In triangle $ABC$ , $O$ is the circumcenter and $I$ is the incenter. $P$ is a point on the exterior angle bisector of $\Delta BAC$ such that $PI \perp OI$ . Extend $PI$ to intersect $BC$ at $Q$ .

Find $\dfrac{PI}{QI}$ .

Note: Figure not drawn to scale.