Let $M$ be a point on the circumscribed circle of the triangle $ABC$, $P,Q,R$ being the projections of $M$ on the sides of the triangle and $P',Q',R'$ the symmetric points of $M$ to this sides of the triangle. Show that the orthocenter of $ABC$ lies on $P'Q'$"

This kind of problem just kept me up at night, I searched a variety of articles on excircles and incircles, <https://en.wikipedia.org/wiki/Incenter>, <https://en.wikipedia.org/wiki/Circumscribed_circle>, <https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle>, I could not find a solution to this.