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circumcenter lies on circumcircle, intersecting circles

Source: JBMO Shortlist 2005

January 1, 2018
geometrycircumcirclesymmetry

Problem Statement

Let C1,C2C_1,C_2 be two circles intersecting at points A,PA,P with centers O,KO,K respectively. Let B,CB,C be the symmetric of AA wrt O,KO,K in circles C1,C2C_1,C_2 respectively. A random line passing through AA intersects circles C1,C2C_1,C_2 at D,ED,E respectively. Prove that the center of circumcircle of triangle DEPDEP lies on the circumcircle of triangle OKPOKP.
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