Question 5
Two circles $\Omega_{1}$ and $\Omega_{2}$ touch internally the circle $\Omega$ in $M$ and $N$ and the center of $\Omega_{2}$ is on $\Omega_{1}$. The common chord of the circles $\Omega_{1}$ and $\Omega_{2}$ intersects $\Omega$ in $A$ and $B$ Lines $MA$ and $MB$ intersects $\Omega_{1}$ in $C$ and $D$. Prove that $\Omega_{2}$ is tangent to $CD$.