Question 118
Consider a circle $C(O)$ and a chord $[MN]$ of this circle. In one of the circular segments determined by the chord $[MN]$ two circles $C_1(O_1)$ and $C_2(O_2)$, $O_1 \neq O_2$, are inscribed, which are tangent to the circle $C(O)$ at the points $A$ and $B$, and to the chord $[MN]$ at the points $C$ and $D$, respectively. Prove that the points $A, B, C$ and $D$ lie on a circle.