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angle chasing inside an isosceles triangle, equal segments and right angle

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p2

April 17, 2020
anglesgeometryisoscelesequal segmentsright angle

Problem Statement

In an isosceles triangle ABCABC (AB=ACAB=AC) on the side BCBC, point MM is marked so that the segment CMCM is equal to the altitude of the triangle drawn on this side, and on the side ABAB, point KK is marked so that the angle KMC\angle KMC is right. Find the angle ACK\angle ACK.