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locus of circumcenters, fixed circle and point not on circle

Source: Sharygin 2006 X-XI CR 22

August 26, 2019
geometryfixedCircumcenterLocus

Problem Statement

Given points A,BA, B on a circle and a point PP not lying on the circle. XX is an arbitrary point of the circle, YY is the intersection point of lines AXAX and BPBP. Find the locus of the centers of the circles circumscribed around the triangles PXYPXY.
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