Answer to Question #5928 in Geometry for nadine

Question

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) ?