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BC tangent ot (DEF) iff BD=//DC - 2014 Cuba 2.6

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September 20, 2024
geometrytangentmidpointisosceles

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC. Points DD, EE and FF are on sides BCBC, CACA and ABAB respectively, such that ∠FDE=∠ABC\angle FDE =\angle ABC and FEFE is not parallel to BCBC. Prove that BCBC is tangent to the circumcircle of the triangle DEFDEF, if and only if, DD is the midpoint of BCBC.
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