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locus of a circumecenter, given a circle lying inside an ellipse

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P20

August 2, 2018
conicsellipseLocusgeometrycircumcircle

Problem Statement

Given are a circle and an ellipse lying inside it with focus CC. Find the locus of the circumcenters of triangles ABCABC, where ABAB is a chord of the circle touching the ellipse.