Question 79
Let $\omega_{1}$ and $\omega_{2}$ be two circles with centres $O_{1}$ and $O_{2}$ respectively. Suppose that $\omega_{1}$ and $\omega_{2}$ intersect at the points $A$ and $B$. The line $(O_{1}A)$ meets the circle $\omega_{2}$ again at $C$, while the line $(O_{2}A)$ meets the circle $\omega_{1}$ again at $D$. Prove that the points $D$, $O_{1}$, $B$, $O_{2}$ and $C$ lie on one circle.