BALKAN-SL 2008 G5

The circle $k_a$ touches the extensions of sides $AB$ and $BC$ , as well as the circumscribed circle of the triangle $ABC$ (from the outside). We denote the intersection of $k_a$ with the circumscribed circle of the triangle $ABC$ by $A'$ . Analogously, we define points $B'$ and $C'$ . Prove that the lines $AA',BB'$ and $CC'$ intersect in one point.