2001 IMO Shortlist Problems/G4
Problem
Let be a point in the interior of triangle
. Let
lie on
with
perpendicular to
. Define
on
and
on
similarly. Define
![$p(M) = \frac {MA' \cdot MB' \cdot MC'}{MA \cdot MB \cdot MC}.$](http://latex.artofproblemsolving.com/2/a/1/2a1fcd37094a33bb1380abb8f62db69ad6af6495.png)
Determine, with proof, the location of such that
is maximal. Let
denote this maximum value. For which triangles
is the value of
maximal?
Solution
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