Geodesic
A note on convex $k$-gons of minimal area circumscribed around a convex $n$-gon
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 33-39

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For one of there $k$-gons of minimal area circumscribed around a convex $n$-gon, $k-1$ sides of the $n$-gon lie on the sides of the $k$-gon. All midpoints of the sides of the $k$-gon belong to the $n$-gon. 
@article{ZNSL_1998_252_a3,
     author = {V. A. Zalgaller},
     title = {A note on convex $k$-gons of minimal area circumscribed around a convex $n$-gon},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--39},
     publisher = {mathdoc},
     volume = {252},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a3/}
}
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V. A. Zalgaller. A note on convex $k$-gons of minimal area circumscribed around a convex $n$-gon. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 33-39. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a3/