Problem

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Tags: geometry, projections, bisects segment, Kharkiv, altitudes



In the acute-angled triangle ABC, let CD,AE be the altitudes. Points F and G are the projections of A and C on the line DE, respectively, H and K are the projections of D and E on the line AC, respectively. The lines HF and KG intersect at point P. Prove that line BP bisects the segment DE.