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Prove that CF < FD

Source: Austrian Mathematical Olympiad 2001, Part 2, D2, P3

June 25, 2011
geometryangle bisectorgeometry proposed

Problem Statement

Let be given a semicircle with the diameter ABAB, and points C,DC,D on it such that AC=CDAC = CD. The tangent at CC intersects the line BDBD at EE. The line AEAE intersects the arc of the semicircle at FF. Prove that CF<FDCF < FD.
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