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Regional Olympiad - FBH 2017 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

September 19, 2018
geometryangle bisectorcircumcircle

Problem Statement

It is given triangle ABCABC. Let internal and external angle bisector of angle ∠BAC\angle BAC intersect line BCBC in points DD and EE, respectively, and circumcircle of triangle ADEADE intersects line ACAC in point FF. Prove that FDFD is angle bisector of ∠BFC\angle BFC
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