I have an interesting "sketch" of a proof of Brahmagupta's formula that I would love to have some help with. It relies on the following lemma:
Lemma: The square of the area for a cyclic quadrilateral Q is a polynomial of Q's sidelengths.
I would really appreciate help in making an proof of the lemma with minimal calculations. Obviously one could prove the above lemma by simply appealing to Brahmagupta's formula, but that would defeat the purpose.
Thank you.