Problem #WSP-00493

Problem

A circle with centre $A$ has the point $B$ on its circumference. A smaller circle is drawn inside this with $AB$ as a diameter and $C$ as its centre. A point $D$ (which is not $B$) is chosen on the circumference of the bigger circle, and the line $BD$ is drawn. $E$ is the point where the line $BD$ intersects the smaller circle.

Show that $|BE|=|DE|$.