Online Geometry Problem 861: Triangle, Incircle, Parallel, Tangent,
Metric Relations. Level: High School,
College,
Mathematics Education

The figure below shows a triangle ABC with
the incircle O tangent to AB, BC, and AC at E, F, and D, respectively.
GH is parallel to AC and tangent to the circle O.If AE = 7, EG = 1, and
FH = 2, find CF.