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Centroamerican Math Olympiad 2017 - P3

Source:

June 23, 2017
OMCCOMCC 2017CENTROgeometrygeometric transformationreflectioncircumcircle

Problem Statement

Let ABCABC be a triangle and DD be the foot of the altitude from AA. Let ll be the line that passes through the midpoints of BCBC and ACAC. EE is the reflection of DD over ll. Prove that the circumcentre of △ABC\triangle ABC lies on the line AEAE.
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