2000 OIM Problems/Problem 2

Problem

Let $S_1$ and $S_2$ be two circles, with centers $O_1$ and $O_2$ respectively, secants in $M$ and $N$ . The line $t$ is the common tangent to $S_1$ and $S_2$ , closest to $M$ . Points $A$ and $B$ are the respective contact points of $t$ with $S_1$ and $S_2$ , $C$ the point diametrically opposite to $B$ and $D$ the point of intersection of the line $O_1O_2$ with the line perpendicular to the line $AM$ drawn by $B$ . Show that $M$ , $D$ , and $C$ are aligned.