In an isosceles trapezoid $ABCD$, the base $AB$ is twice as large as the base $CD$. Point $M$ is the midpoint of $AB$. It is known that the center of the circle inscribed in the triangle $MCB$ lies on the circle circumscribed around the triangle $MDC$. Find the angle $\angle MBC$.
Problem
Source: V.A. Yasinsky Geometry Olympiad 2020 X-XI p4 , Ukraine
Tags: geometry, incenter, circumcircle, trapezoid, isosceles
