SILK-ROAD 2005 Problem 3

Assume $A,B,C$ are three collinear points that $B \in [AC]$ . Suppose $AA'$ and $BB'$ are to parrallel lines that $A'$ , $B'$ and $C$ are not collinear. Suppose $O_1$ is circumcenter of circle passing through $A$ , $A'$ and $C$ . Also $O_2$ is circumcenter of circle passing through $B$ , $B'$ and $C$ . If area of $A'CB'$ is equal to area of $O_1CO_2$ , then find all possible values for $\angle CAA'$