$ABC$ is an acute triangle. Points $M$ and $K$ on side $AC$ are such that $\angle ABM = \angle CBK$. Prove that the circumcenters of triangles $ABM$, $ABK$, $CBM$ and $CBK$ are concyclic. (Author: T. Emelyanova)
Problem
Source: Problem 2 of Russian Regional Olympiad 2011, grade 10
Tags: geometry, circumcircle, geometric transformation, rotation, geometry proposed