Hello all, can someone please provide me some help with an optimal design question. Any sort of help would be awesome.
Q1) Show that among all the 4-sided polygons inscribed in a circle the squares have the largest area.
Q2) And for fixed n which is the n-gon of largest area inscribed in a circle?
For Q1 I know I should focus on showing that all sides of a quadrilateral of maximal area have to be of equal length. So I would use Brahmagupta's formula I think, but how would I show that the squares have the largest area?
Q2) I don't know how to approach this.
Thank you all for any help.