19. A right angle rotates around its vertex. Find the geometric locus of the midpoints of the segments connecting the points of intersection of the sides of the angle and a given circle.

## 9th grade
63.19. Answer. Let $O$ be the center of the given circle, $R$ its radius, and $C$ the vertex of the angle. Then the geometric locus of points specified in the condition is a circle with center at the midpoint of segment $O C$ and diameter $\sqrt{2 R^{2}-|O C|^{2}}$.