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Geometry Problem 939: Circle, Tangent, Secant, Chord, Parallel, Midpoint. Level: High School, College, Mathematics Education

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AB and AC are tangent to a circle O (see figure below). Chord CD is parallel to AB and secant AD meets the circle O at E. If CE extended meets AB at F, prove that F is the midpoint of AB.
 
 

Geometry Problem 939: Circle, Tangent, Secant, Chord, Parallel, Midpoint

 

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