NL-NWO 2004 Problem 4

Two circles $C_1$ and $C_2$ touch each other externally in a point $P$ . At point $C_1$ there is a point $Q$ such that the tangent line in $Q$ at $C_1$ intersects the circle $C_2$ at points $A$ and $B$ . The line $QP$ still intersects $C_2$ at point $C$ . Prove that triangle $ABC$ is isosceles.