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OD _ |_ AB wanted, 2 circumrcircles

Source: 2010 Brasil IMO TST 3.1

July 23, 2021
perpendiculargeometry

Problem Statement

Let ABCABC be an acute triangle and DD a point on the side ABAB. The circumcircle of triangle BCDBCD cuts the side ACAC again at EE .The circumcircle of triangle ACDACD cuts the side BCBC again at FF. If OO is the circumcenter of the triangle CEFCEF. Prove that ODOD is perpendicular to ABAB.
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