Geometry Problem 1485: Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement

The figure shows a triangle ABC with orthocenter H. AT is tangent to the circle with diameter BC, TH extended meets the circle at F. If AH = 20, HE = 7, and TH = 16, find the measure of HF.
Geometry Problem 1485: Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement

Orthocenter

The orthocenter of a triangle is the point of intersection of the altitudes.