This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2007 Nicolae Coculescu, 4
Let $ M $ be a point in the interior of a triangle $ ABC, $ let $ D $ be the intersection of $ AM $ with $ BC, $ let $ E $ be the intersection of $ M $ with AC, let $ F $ be the intersection of $ CM $ with $ AB. $ Knowing that the expression $$ \frac{MA}{MD}\cdot \frac{MB}{ME}\cdot \frac{MC}{MF} $$ is minimized, describe the point $ M. $
infimum geometry locus analytic geometry algebra

2019 Ramnicean Hope, 2
Calculate $ \inf_{x> 0} \sqrt{(1+x)^2+4/x} . $ [i]Constantin Rusu[/i] and [i]Mihai Neagu[/i]
function graphing infimum real analysis AM-GM inequality