5.2.5.11 Locus of Points

Condition: inside the circle, an arbitrary point \ (m \), different from the center of the circle, is taken. For each chord of a circle passing through \ (m \) and different from the diameter, we denote the point of intersection of the tangents to the circle through the ends of this chord through \ (C \). To prove that the geometric place of points \ (C \) is a straight line.