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circumcenter coincides with excenter , <A=45^o

Source: 2014 Oral Moscow Geometry Olympiad grades 8-9 p1

August 9, 2019
geometryCircumcenterexcenter

Problem Statement

In triangle ABC,∠A=45o,BHABC, \angle A= 45^o, BH is the altitude, the point KK lies on the ACAC side, and BC=CKBC = CK. Prove that the center of the circumscribed circle of triangle ABKABK coincides with the center of an excircle of triangle BCHBCH.
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