8. Given a circle and a point $A$ outside it. Let the circle passing through $A$ touch the given one at an arbitrary point $B$, and the tangents to it, drawn through points $A$ and $B$, intersect at point $M$. Find the geometric locus of points $M$.
8. If $B$ is the point of tangency, and $O$ is the center of the given circle, then $|O M|^{2}-|A M|^{2}=|O M|^{2}-|B M|^{2}=|O B|^{2}=R^{2}$. Therefore, $M$ lies on the line perpendicular to $O A$ (see problem II.1).