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Excenters and Extouch

Source: 2013 CWMI

August 18, 2013
geometrygeometric transformationreflectionpower of a pointradical axisgeometry unsolved

Problem Statement

Let ABCABC be a triangle, and B1,C1B_1,C_1 be its excenters opposite B,CB,C. B2,C2B_2,C_2 are reflections of B1,C1B_1,C_1 across midpoints of AC,ABAC,AB. Let DD be the extouch at BCBC. Show that ADAD is perpendicular to B2C2B_2C_2
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