177. 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 from points $A$ and $B$, intersect at point $M$. Find the set of points $M$.
177. If $B$ is the point of tangency, and $O$ is the center of the given circle, then

$$
\mid O M^{2}-A M^{2}=O M^{2}-B M^{2}=O B^{2}=R^{2}
$$

Thus, $M$ lies on the line perpendicular to $O A$ (see problem 170).