Geometry Problem 940: Circle, Tangent, Secant, Chord, Parallel, Perpendicular, 90 Degrees, Midpoint. Level: High School, College, Mathematics Education

AB and AC are tangent to a circle O (see figure below). Chord BF is parallel to a secant ADE. If chord CF meets ADE at H, prove that (1) OH is perpendicular to ADE, (2) H is the midpoint of DE.