KöMaL 2006 B3910

$AB$ is a diameter in the circle $k$. Choose an arbitrary point $E$ in the interior of the circle. The other intersections of the lines $AE$ and $BE$ with the circle are $C$ and $D$, respectively. Prove that the value of the expression $AC^. AE$+$BD^. BE$ is independent of the position of $E$.