Two Triangles Centers At Play

Geometry Level 2

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.

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