Problem

Source: Czech-Polish-Slovak Junior Match 2014, Individual p1 CPSJ

Tags: equal segments, geometry, circles, parallelogram



On the plane circles $k$ and $\ell$ are intersected at points $C$ and $D$, where circle $k$ passes through the center $L$ of circle $\ell$. The straight line passing through point $D$ intersects circles $k$ and $\ell$ for the second time at points $A$ and $B$ respectively in such a way that $D$ is the interior point of segment $AB$. Show that $AB = AC$.