JBMO 2008 Problem 2

The vertices $A$ and $B$ of an equilateral triangle $ABC$ lie on a circle $k$ of radius $1$, and the vertex $C$ is in the interior of the circle $k$. A point $D$, different from $B$, lies on $k$ so that $AD=AB$. The line $DC$ intersects $k$ for the second time at point $E$. Find the length of the line segment $CE$.