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Prove that AFE and CBD are similar [Slovenia 2010]

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November 14, 2010
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be an acute triangle. A line parallel to BCBC intersects the sides ABAB and ACAC at DD and EE, respectively. The circumcircle of the triangle ADEADE intersects the segment CDCD at F (F≠D).F \ (F \neq D). Prove that the triangles AFEAFE and CBDCBD are similar.
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