Answer to Question #5928 in Geometry for nadine

Question #5928
A and B are two fixed points of a circle C(O,R) m is a variable point of the circle (C) . [MI] and [AR] are two heights of the triangle AMB . H is the orthocenter of the triangle AMB the line (MH) cuts the circle (c) again at E prove that the triangles BIM , HAL and AIE are similar . verify that the line (AB) is perpendicular bisector OF [HE]. designate by o' the point so that (AB) is the perpendicular bisector of [OO'] . verify that OHEO' is an isosceles trapezoid and that O'H equal to the radius r . what is the geometric locus of H when M describes the circle (C) ?
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