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Circles intersect on altitude of ABC -IMO Long List P3

Source:

August 28, 2010
geometrypower of a pointradical axisgeometry proposed

Problem Statement

A line parallel to the side BCBC of a triangle ABCABC meets ABAB in FF and ACAC in EE. Prove that the circles on BEBE and CFCF as diameters intersect in a point lying on the altitude of the triangle ABCABC dropped from AA to BC.BC.
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