Let ABCD be a cyclic quadrilateral whose side AB is at the same time the diameter of the circle. The lines AC and BD intersect at point E and the extensions of lines AD and BC intersect at point F. Segment EF intersects the circle at G and the extension of segment EF intersects AB at H. Show that if G is the midpoint of FH, then E is the midpoint of GH. cyclic quadrilateralmidpointcirclegeometry