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.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe15.htm