National Math Olympiad

Let $K_1$ and $K_2$ be the circles centered at $O_1$ and $O_2$, respectively, meeting at the points $A$ and $B$. Let $p$ be the line through the point $A$ meeting the circles $K_1$ and $K_2$ again at $C_1$ and $C_2$. Assume that $A$ lies between $C_1$ and $C_2$. Denote the intersection of the lines $C_1{O}_1$ and $C_2{O}_2$ by $D$. Prove that the points $C_1,C_2,B$ and $D$ lie on the same circle.