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2001 IMO Shortlist Problems/G4

Revision as of 18:46, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Let <math>M</math> be a point in the interior of triangle <math>ABC</math>. Let <math>A'</math> lie on <math>BC</math> with <math>MA'</math> perpendicular to <math>BC</math>....)
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Problem

Let $M$ be a point in the interior of triangle $ABC$. Let $A'$ lie on $BC$ with $MA'$ perpendicular to $BC$. Define $B'$ on $CA$ and $C'$ on $AB$ similarly. Define

$p(M) = \frac {MA' \cdot MB' \cdot MC'}{MA \cdot MB \cdot MC}.$

Determine, with proof, the location of $M$ such that $p(M)$ is maximal. Let $\mu(ABC)$ denote this maximum value. For which triangles $ABC$ is the value of $\mu(ABC)$ maximal?

Solution

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Resources

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