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Area inequality with brocard point

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December 31, 2011
geometryinequalitiescircumcircletrigonometrygeometry unsolved

Problem Statement

Let PP be a point inside a triangle ABCABC such that ∠PAB=∠PBC=∠PCA\angle P AB = \angle P BC = \angle P CA Suppose AP,BP,CPAP, BP, CP meet the circumcircles of triangles PBC,PCA,PABP BC, P CA, P AB at X,Y,ZX, Y, Z respectively (≠P)(\neq P) . Prove that [XBC]+[YCA]+[ZAB]≥3[ABC][XBC] + [Y CA] + [ZAB] \ge 3[ABC]
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