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Geometry with iff

Source: 2015 JBMO TST - Macedonia, Problem 4

December 31, 2015
geometrycircumcircleangle bisector

Problem Statement

Let △ABC\triangle ABC be an acute angled triangle and let kk be its circumscribed circle. A point OO is given in the interior of the triangle, such that CE=CFCE=CF, where EE and FF are on kk and EE lies on AOAO while FF lies on BOBO. Prove that OO is on the angle bisector of ∠ACB\angle ACB if and only if AC=BCAC=BC.
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