BG-MO 1964 Problem 3

There are given two intersecting lines $g_1,g_2$ and a point $P$ in their plane such that $\angle(g1,g2)\ne90^\circ$ . Its symmetrical points on any point $M$ in the same plane with respect to the given lines are $M_1$ and $M_2$ . Prove that:

(a) the locus of the point $M$ for which the points $M_1,M_2$ and $P$ lie on a common line is a circle $k$ passing through the intersection point of $g_1$ and $g_2$ . (b) the point $P$ is an orthocenter of a triangle, inscribed in the circle $k$ whose sides lie at the lines $g_1$ and $g_2$ .