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triangle given H, M(AB), midpoint of foot

Source: Bulgaria 1966 P3

June 23, 2021
geometryTriangles

Problem Statement

(a) In the plane of the triangle ABCABC, 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 ABCABC if it is known the positions of the orthocenter HH, midpoint of the side ABAB and the midpoint of the segment joining the feet of the heights through vertices AA and BB.