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Find the location when Sigma is maximal - ILL 1990 USS4

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September 19, 2010
geometry unsolvedgeometry

Problem Statement

The side-lengths of two equilaterals ABCABC and KLMKLM are 11 and 1/41/4, respectively. And triangle KLMKLM located inside triangle ABCABC. Denote by Σ\Sigma the sum of the distances from AA to lines KL,LMKL, LM and MKMK. Find the location of triangle KLMKLM when Σ\Sigma is maximal.
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