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CSMO Grade 11 Problem 6

Source: CSMO Grade 11 Problem 6

August 6, 2017
geometry

Problem Statement

Let ABCDABCD be a cyclic quadrilateral inscribed in circle OO, where ACBDAC\perp BD. MM be the midpoint of arc ADCADC. Circle (DOM)(DOM) intersect DA,DCDA,DC at E,FE,F. Prove that BE=BFBE=BF.