Geodesic
On Maximal Perimeter of a Convex Pentagon with a Fixed Diameter
Matematičeskoe obrazovanie, no. 1 (2010), pp. 12-16 
F. L. Varpakhovskii; O. Logvinenko. On Maximal Perimeter of a Convex Pentagon with a Fixed Diameter. Matematičeskoe obrazovanie, no. 1 (2010), pp. 12-16. http://geodesic.mathdoc.fr/item/MO_2010_1_a2/
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     author = {F. L. Varpakhovskii and O. Logvinenko},
     title = {On {Maximal} {Perimeter} of a {Convex} {Pentagon} with a {Fixed} {Diameter}},
     journal = {Matemati\v{c}eskoe obrazovanie},
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     year = {2010},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2010_1_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the regular pentagon has the maximal perimeter among all of the convex pentagons with a fixed diameter.