Question 5
(ROM) Given a triangle $OAB$ such that $\angle AOB=\alpha\lt 90^\circ$, let $M$ be an arbitrary point of the triangle different from $O$. Denote by $P$ and $Q$ the feet of the perpendiculars from $M$ to $OA$ and $OB$, respectively. Let $H$ be the orthocenter of the triangle $OPQ$. Find the locus of points $H$ when:
(a) $M$ belongs to the segment $AB$;
(b) $M$ belongs to the interior of $\triangle OAB$.
(a) $M$ belongs to the segment $AB$;
(b) $M$ belongs to the interior of $\triangle OAB$.