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Circumcentres make a parallelogram

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November 1, 2010
geometryparallelogrammodular arithmeticcircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

In a triangle ABCABC with AB<AC<BCAB<AC<BC, the perpendicular bisectors of ACAC and BCBC intersect BCBC and ACAC at KK and LL, respectively. Let OO, O1O_1, and O2O_2 be the circumcentres of triangles ABCABC, CKLCKL, and OABOAB, respectively. Prove that OCO1O2OCO_1O_2 is a parallelogram.
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