246. Given a circle $S$ and a point $M$ outside it. Through the point $M$ a variable circle $\Sigma$ is drawn, intersecting $S$ at points $A, B$. Find the geometric locus of the points of intersection of the line $A B$ with the tangent to $\Sigma$ at the point $M$.
246. If $P$ is a point of the required geometric locus, then $P A \cdot P B = P M^2$ (by the property of the tangent and secant of a circle). Therefore, the power $P A \cdot P B$ of point $P$ with respect to $S$ is equal to the power $P M^2$ of this point with respect to point $M$ (see above, p. 222). It follows that $P$ belongs to the radical axis $r$ of point $M$ and circle $S$.[^71]