BALKAN-SL 2010 G8

Let $c(0, R)$ be a circle with diameter $AB$ and $C$ a point, on it different than $A$ and $B$ such that $\angle AOC > 90^o$ . On the radius $OC$ we consider the point $K$ and the circle $(c_1)$ with center $K$ and radius $KC = R_1$ . We draw the tangents $AD$ and $AE$ from $A$ to the circle $(c_1)$ . Prove that the straight lines $AC, BK$ and $DE$ are concurrent