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.
by
Bolin Chen