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Isosceles triangle geo

Source: Serbia JBMO TST 2023 P1

May 28, 2023
geometry

Problem Statement

Given is an isosceles triangle ABCABC with CA=CBCA=CB and angle bisector BDBD, DāˆˆACD \in AC. The line through the center OO of (ABC)(ABC), perpendicular to BDBD, meets BCBC at EE. The line through EE, parallel to BDBD, meets ACAC at FF. Prove that CE=DFCE=DF.
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