Geometry Problem 1365: Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps.

Proposition

In the figure below, AB and AC are tangent to a circle O and ADE is a secant. Chord CF is parallel to AE. Chord BF and AE intersect at M. Prove that M is the midpoint of DE.
 

 

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Sketch and Typography of problem 1365 using iPad Apps