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p(M ) = \frac{MA′ . MB′ . MC ′ }{MA. MB.MC}

Source: 13-th Hungary-Israel Binational Mathematical Competition 2002

April 7, 2007
trigonometrygeometryincenterinequalitiesgeometry proposed

Problem Statement

Let A′,B′,C′A', B' , C' be the projections of a point MM inside a triangle ABCABC onto the sides BC,CA,ABBC, CA, AB, respectively. Define p(M)=MA′⋅MB′⋅MC′MA⋅MB⋅MCp(M ) = \frac{MA'\cdot MB'\cdot MC'}{MA \cdot MB \cdot MC} . Find the position of point MM that maximizes p(M)p(M ).
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