BALKAN-SL 2013 G4

Let $c(O, R)$ be a circle, $AB$ a diameter and $C$ an arbitrary point on the circle different than $A$ and $B$ such that $\angle AOC > 90^o$ . On the radius $OC$ we consider point $K$ and the circle $c_1(K, KC)$ . The extension of the segment $KB$ meets the circle $(c)$ at point $E$ . From $E$ we consider the tangents $ES$ and $ET$ to the circle $(c_1)$ . Prove that the lines $BE, ST$ and $AC$ are concurrent.