In an isosceles triangle $ABC$ ($AB=AC$) on the side $BC$, point $M$ is marked so that the segment $CM$ is equal to the altitude of the triangle drawn on this side, and on the side $AB$, point $K$ is marked so that the angle $\angle KMC$ is right. Find the angle $\angle ACK$.
Problem
Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p2
Tags: angles, geometry, isosceles, equal segments, right angle