BG-MO 1966 Problem 3

(a) In the plane of the triangle $ABC$ , find a point with the following property: its symmetrical points with respect to the midpoints of the sides of the triangle lie on the circumscribed circle. (b) Construct the triangle $ABC$ if it is known the positions of the orthocenter $H$ , midpoint of the side $AB$ and the midpoint of the segment joining the feet of the heights through vertices $A$ and $B$ .