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Concyclic points and a bisector

Source: Saint Petersburg MO 2020 Grade 11 Problem 3

May 7, 2020
geometryangle bisectorincenterperpendicular bisectorcircumcircle

Problem Statement

BB1BB_1 is the angle bisector of △ABC\triangle ABC, and II is its incenter. The perpendicular bisector of segment ACAC intersects the circumcircle of △AIC\triangle AIC at DD and EE. Point FF is on the segment B1CB_1C such that AB1=CFAB_1=CF.Prove that the four points B,D,EB, D, E and FF are concyclic.
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