Question 59
Let $A$, $B$, $C$ be three collinear points such that the point $B$ lies between $A$ and $C$. Let $AA'$ and $BB'$ be parallel lines such that the points $A'$ and $B'$ lie on the same side of the line $AB$, and $A'$, $B'$, $C$ are not collinear. Let $O_1$ be the center of the circle passing through the points $A$, $A'$, $C$, and $O_2$ be the center of the circle passing through the points $B$, $B'$, $C$. Find all possible values of the angle $CAA'$, if triangles $A'CB'$ and $O_1CO_2$ have the same area.