Work out cyclic quadrilateral instantly with clear inputs, formula shown and shareable results.
Brahmagupta's formula gives the maximum area for four given side lengths, achieved exactly when the quadrilateral is cyclic: A = √[(s−a)(s−b)(s−c)(s−d)]. The circumradius follows from Parameshvara's formula.
Brahmagupta
A = √[(s−a)(s−b)(s−c)(s−d)], s = (a+b+c+d)/2
Parameshvara
R = √[(ab+cd)(ac+bd)(ad+bc)] / (4A)
All four vertices lie on one circle, which happens exactly when opposite angles sum to 180°.
It is the four-sided generalisation. Setting d = 0 collapses Brahmagupta's formula back to Heron's.