Question 68
Two circles touch each other externally at point $C$. Consider two diameters $A_1A_2$, $B_1B_2$ of the same direction. Circle with the center on the common internal tangent passes through the point of intersection of $A_1B_2$, $A_2B_1$, and meets these lines at points $M$, $N$. Prove that $MN$ is perpendicular to $A_1A_2$, $B_1B_2$.