KMO 2008 Problem 3

Points $A,B,C,D,E$ lie in a counterclockwise order on a circle $O$ , and $AC = CE$ $P=BD \cap AC$ , $Q=BD \cap CE$ Let $O_1$ be the circle which is tangent to $\overline {AP}, \overline {BP}$ and arc $AB$ (which doesn't contain $C$ ) Let $O_2$ be the circle which is tangent $\overline {DQ}, \overline {EQ}$ and arc $DE$ (which doesn't contain $C$ ) Let $O_1 \cap O = R, O_2 \cap O = S, RP \cap QS = X$ Prove that $XC$ bisects $\angle ACE$