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Area Inequality

Source: China TST 2004 Quiz

February 1, 2009
geometryinequalitiescircumcirclegeometry unsolved

Problem Statement

Find the largest value of the real number λ \lambda, such that as long as point P P lies in the acute triangle ABC ABC satisfying \angle{PAB}\equal{}\angle{PBC}\equal{}\angle{PCA}, and rays AP AP, BP BP, CP CP intersect the circumcircle of triangles PBC PBC, PCA PCA, PAB PAB at points A1 A_1, B1 B_1, C1 C_1 respectively, then S_{A_1BC}\plus{} S_{B_1CA}\plus{} S_{C_1AB} \geq \lambda S_{ABC}.
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