Problem

Source: Sharyging 2005 finals 11.5

Tags: geometry, Fixed point, fixed, angle



The angle and the point $K$ inside it are given on the plane. Prove that there is a point $M$ with the following property: if an arbitrary line passing through intersects the sides of the angle at points $A$ and $B$, then $MK$ is the bisector of the angle $AMB$.