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Problem 2 -- Orthocenter and Circumcenter

Source: 47th Austrian Mathematical Olympiad National Competition Part 1 Problem 2

July 28, 2018
geometryAustriaorthocenterCircumcentercircumcircle

Problem Statement

We are given an acute triangle ABCABC with AB>ACAB > AC and orthocenter HH. The point EE lies symmetric to CC with respect to the altitude AHAH. Let FF be the intersection of the lines EHEH and ACAC. Prove that the circumcenter of the triangle AEFAEF lies on the line ABAB.
(Karl Czakler)
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