Question 6
Two circles with centers $O_1,O_2$ and unequal radii are externally tangent at $A$. Let $M$ be inside the circle centered at $O_2$, with $M$ not on line $O_1O_2$. Find a line $d$ through $M$ such that the circle $ABC$ is tangent to $O_1O_2$, where $B$ is an intersection of $d$ with the circle centered at $O_1$, and $C$ is an intersection of $d$ with the circle centered at $O_2$.