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Turkey NMO 2000 Problem 1, locus of point P_B

Source: Turkey NMO 2000 Problem 1

September 29, 2011
trigonometrygeometryperpendicular bisectorgeometry proposed

Problem Statement

A circle with center OO and a point AA in this circle are given. Let PBP_{B} is the intersection point of [AB][AB] and the internal bisector of ∠AOB\angle AOB where BB is a point on the circle such that BB doesn't lie on the line OAOA, Find the locus of PBP_{B} as BB varies.
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