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Orthocentres lying on the circumcircle

Source: IMOTC 2014 Practice Test 1 Problem 3

July 11, 2014
geometrycircumcirclegeometric transformationtrigonometryfunctionangle bisectorgeometry unsolved

Problem Statement

In a triangle ABCABC, points XX and YY are on BCBC and CACA respectively such that CX=CYCX=CY,AXAX is not perpendicular to BCBC and BYBY is not perpendicular to CACA.Let Γ\Gamma be the circle with CC as centre and CXCX as its radius.Find the angles of triangle ABCABC given that the orthocentres of triangles AXBAXB and AYBAYB lie on Γ\Gamma.
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