BG-MO 1978 Problem 2

$k_1$ denotes one of the arcs formed by intersection of the circumference $k$ and the chord $AB$ . $C$ is the middle point of $k_1$ . On the half line (ray) $PC$ is drawn the segment $PM$ . Find the locus formed from the point $M$ when $P$ is moving on $k_1$ .

G. Ganchev