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Altitudes and sides

Source: St Petersburg Olympiad 2009, Grade 9, P5

August 30, 2017
geometry

Problem Statement

ABCABC is acute-angled triangle. AA1,BB1,CC1AA_1,BB_1,CC_1 are altitudes. X,YX,Y - midpoints of AC1,A1CAC_1,A_1C. XY=BB1XY=BB_1. Prove that one side of ABCABC in 2\sqrt{2} greater than other side.
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