7.13. Given two points $A$ and $B$. Two circles touch the line $A B$ (one at point $A$, the other at point $B$) and touch each other at point $M$. Find the locus of $M$.
7.13. Let's draw a common tangent through point $M$ to the circles. Let $O$ be the point of intersection of this tangent with the line $A B$. Then $A O = M O = B O$, i.e., $O$ is the midpoint of segment $A B$. Point $M$ lies on a circle with center $O$ and radius $A B / 2$. The set of points $M$ is a circle with diameter $A B$ (points $A$ and $B$ should be excluded).