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Line through orthocenter

Source: Mexico National Olympiad 2011 Problem 2

June 22, 2014
geometrycircumcirclegeometric transformationreflectionpower of a pointperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be an acute triangle and Γ\Gamma its circumcircle. Let ll be the line tangent to Γ\Gamma at AA. Let DD and EE be the intersections of the circumference with center BB and radius ABAB with lines ll and ACAC, respectively. Prove the orthocenter of ABCABC lies on line DEDE.
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