Problem #PRU-5176

Problem

Two circles with centres $A$ and $C$ are tangent to each other at the point $B$. Two points $D$ and $E$ are chosen on the circles in such a way that a segment $DE$ passes through the point $B$. Prove that the tangent line to one circle at the point $D$ is parallel to the tangent line to the other circle at the point $E$.