MathDB
Geometric inequality

Source: JBMO Shortlist 2002

November 12, 2008
inequalitiesgeometrycircumcirclegeometry proposed

Problem Statement

Let ABC ABC be a triangle with area S S and points D,E,F D,E,F on the sides BC,CA,AB BC,CA,AB. Perpendiculars at points D,E,F D,E,F to the BC,CA,AB BC,CA,AB cut circumcircle of the triangle ABC ABC at points (D1,D2),(E1,E2),(F1,F2) (D_1,D_2), (E_1,E_2), (F_1,F_2). Prove that: |D_1B\cdot D_1C \minus{} D_2B\cdot D_2C| \plus{} |E_1A\cdot E_1C \minus{} E_2A\cdot E_2C| \plus{} |F_1B\cdot F_1A \minus{} F_2B\cdot F_2A| > 4S
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