Question 2
Two circles $C_1,C_2$ touch externally at $M$, and the radius of $C_2$ is greater than that of $C_1$. A point $A$ moves on $C_2$ and is not on the line through the two centers. Points $B,C$ on $C_1$ are chosen so that $AB,AC$ are tangent to $C_1$. Lines $BM,CM$ meet $C_2$ again at $E,F$, respectively. Let $D$ be the intersection of the tangent at $A$ and the line $EF$. Prove that the locus of $D$ as $A$ varies is a straight line.