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Angle bisector, median and foot of altitude

Source: Germany Bundeswettbewerb Mathematik 2008, Round 1, Problem 3

July 19, 2008
geometryangle bisectorgeometry unsolved

Problem Statement

Prove: In an acute triangle ABC ABC angle bisector wα, w_{\alpha}, median sb s_b and the altitude hc h_c intersect in one point if wα, w_{\alpha}, side BC BC and the circle around foot of the altitude hc h_c have vertex A A as a common point.
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