MathDB
Cool cevians problem

Source: 1996 IMO Shortlist

March 28, 2006
trigonometrytrig identitiesLaw of CosinesIMO Shortlist

Problem Statement

Let ABCABC be an equilateral triangle and let PP be a point in its interior. Let the lines APAP, BPBP, CPCP meet the sides BCBC, CACA, ABAB at the points A1A_1, B1B_1, C1C_1, respectively. Prove that A1B1⋅B1C1⋅C1A1≥A1B⋅B1C⋅C1AA_1B_1 \cdot B_1C_1 \cdot C_1A_1 \ge A_1B \cdot B_1C \cdot C_1A.
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