I want to prove that there is no maximum perimeter trapezoid inscribed in a circle.
Edit: the way my textbook defined a trapezoid does not allow for a square to fit in the trapezoid definition. If your definition is different than that, this problem is the equivalent of proving that the maximum perimeter trapezoid inscribed in a circle is a square.
What I have already figured:
I know (and know how to prove) that an inscribed trapezoid must be an isosceles trapezoid.
I also know that the maximum perimeter quadrilateral inscribed in a circle is a square (but don't know how to prove it).
I know that the inscribed trapezoid can get as close to being a square as we like, but it can never be a square. That is why there is no maximum perimeter inscribed trapezoid. But I do not know how to prove that the square is the maximum perimeter quadrilateral inscribed in a circle.
I think that I should approximate the inscribed square by an inscribed trapezoid, but when I tried that I couldn't prove that the perimeter of the square was greater than that of the trapezoid.