FI-MO 2009 Problem 3

The circles $\mathcal{Y}_0$ and $\mathcal{Y}_1$ lies outside each other. Let $O_0$ be the center of $\mathcal{Y}_0$ and $O_1$ be the center of $\mathcal{Y}_1$ . From $O_0$ , draw the rays which are tangents to $\mathcal{Y}_1$ and similarty from $O_1$ , draw the rays which are tangents to $\mathcal{Y}_0$ . Let the intersection points of rays and circle $\mathcal{Y}_i$ be $A_i$ and $B_i$ . Show that the line segments $A_0B_0$ and $A_1B_1$ have equal lengths.