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Some Inequalities Between two Polygons Inscribed one in
the Other Aurelio de Gennaro Abstract.
It is well known that, given a triangle inscribed in another triangle, the
perimeters of the three external triangles can never all be simultaneously
greater than the perimeter of the inscribed triangle and that furthermore
they are all equal to it if and only if we put the vertices of the
inscribed triangle at the midpoints of sides of the circumscribed triangle.
The same result is true for the areas. The present paper shows how such a
results extends to the case of two convex polygons inscribed one in other,
connecting it to the classic works about inscribed and circumscribed
polygons respectively with minimum and maximum perimeter.