Online Geometry Problem 795: Intersecting Circles, Common Chord,
Midpoint, Tangent, Secant Line, Perpendicular, 90
Degrees. Level: High School,
SAT Prep, College,
Mathematics Education

The circles O and Q intersect at A and B
(see the figure). M is the midpoint of AB and CAD is a secant line. The
tangents at C and D meet at E. BF is perpendicular to CE and BG is
perpendicular to DE. If FG cuts CD at H, prove that MH is perpendicular
to FG.