$AD$ and $BE$ are the altitudes of the triangle $ABC$. It turned out that the point $C'$, symmetric to the vertex $C$ wrt to the midpoint of the segment $DE$, lies on the side $AB$. Prove that $AB$ is tangent to the circle circumscribed around the triangle $DEC'$.
Problem
Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p1
Tags: geometry, circumcircle, tangent, symmetry