VWO 2003 Problem 2

Two circles $C_1$ and $C_2$ intersect at $S$ . The tangent in $S$ to $C_1$ intersects $C_2$ in $A$ different from $S$ . The tangent in $S$ to $C_2$ intersects $C_1$ in $B$ different from $S$ . Another circle $C_3$ goes through $A, B, S$ . The tangent in $S$ to $C_3$ intersects $C_1$ in $P$ different from $S$ and $C_2$ in $Q$ different from $S$ . Prove that the distance $PS$ is equal to the distance $QS$ .

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