## Τρίτη, 10 Οκτωβρίου 2017

### 2008 JBMO Shortlist G3 problem 2

The vertices $A$ and $B$ of an equilateral $\vartriangle ABC$ lie on a circle $k$ of radius $1$, and the vertex $C$ is inside $k$. The point $D \ne B$ lies on $k$, $AD = AB$ and the line $DC$ intersects $k$ for the second time in point $E$. Find the length of the segment $CE$.

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