A note on convex $k$-gons of minimal area circumscribed around a convex $n$-gon

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.