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AE = CF iff BD bisects <ABC, 2 circumcircles 2019 Ecuador NMO (OMEC) 3.2

Source:

September 18, 2021
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle and DD be a point on segment ACAC. The circumscribed circle of the triangle BDCBDC cuts ABAB again at EE and the circumference circle of the triangle ABDABD cuts BCBC again at FF. Prove that AE=CFAE = CF if and only if BDBD is the interior bisector of ∠ABC\angle ABC.
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