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Locus of Intersection of Angle and Perpendicular Bisectors

Source: Sharygin Geometry Olympiad 2014 - Problem 6

November 15, 2014
geometryperpendicular bisectorgeometry unsolved

Problem Statement

Given a circle with center OO and a point PP not lying on it, let XX be an arbitrary point on this circle and YY be a common point of the bisector of angle POXPOX and the perpendicular bisector to segment PXPX. Find the locus of points YY.
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