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XY \cdot YZ\cdot ZX \ge XB\cdot YC\cdot ZA, equilateral

Source: Switzerland - Swiss TST 1998 p8

February 19, 2020
geometryProductEquilateral

Problem Statement

Let △ABC\vartriangle ABC be an equilateral triangle and let PP be a point in its interior. Let the lines AP,BP,CPAP,BP,CP meet the sides BC,CA,ABBC,CA,AB in the points X,Y,ZX,Y,Z respectively. Prove that XY⋅YZ⋅ZX≥XB⋅YC⋅ZAXY \cdot YZ\cdot ZX \ge XB\cdot YC\cdot ZA.
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