Prove that the polygon of $n$ sides with the bigger area, inscribed in a circumference, is always a regular polygon.
Ex (because the way in which I wrote the statement maybe was not clear and produces confusion): For $n=4$: Prove that the inscribed quadrilateral with bigger area is always a square.
I thought that this problem was easy, but i don't see the way to prove this
Any hints?
Edit This problem is mean to be solved without trigonometry, so the post linked as duplicated doesn't help me
