I'm trying to prove that a 'tangential' quadrilateral (i.e. one with an in-circle) whose area is given by Brahmagupta's formula for a cyclic quadrilateral is also cyclic (and thus 'bicentric').
2026-03-29 21:35:24.1774820124
Bicentric quadrilaterals
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I've just realised that, stated as a theorem, the Brahmagupta condition has a converse:
A cyclic quadrilateral has the largest area for the lengths of its sides. This means any particular quadrilateral satisfying the condition is unique, and therefore cyclic.
I'm therefore withdrawing my problem.