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Orthocenter of an acute triangle

Source: Dutch IMO TST II Problem 3

July 17, 2014
geometrycircumcirclegeometric transformationreflectiontrapezoidgeometry unsolved

Problem Statement

Let HH be the orthocentre of an acute triangle ABCABC. The line through AA perpendicular to ACAC and the line through BB perpendicular to BCBC intersect in DD. The circle with centre CC through HH intersects the circumcircle of triangle ABCABC in the points EE and FF. Prove that ∣DE∣=∣DF∣=∣AB∣|DE| = |DF| = |AB|.
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