5.2.5.11 Locus of points

Condition: An arbitrary point \(M\) is taken inside the circle, different from the center of the circle. For each chord of a circle passing through \( M \) and different from the diameter, we denote by \( C \) the point of intersection of the tangents to the circle drawn through the ends of this chord. Prove that the locus of points \( C \) is a straight line.