= \frac{4(s-a)(s-b)(s-c)(s-d)}{(ad+bc)^2}; \tan \frac{A}{2} = \sqrt{\frac{(s-a)(s-d)}{(s-b)(s-c)}}. Four lines, each perpendicular to one side of a cyclic quadrilateral and passing through the opposite side's midpoint, are concurrent . Properties of cyclic quadrilaterals that are also orthodiagonal Brahmagupta's theorem states that for a cyclic quadrilateral that is also orthodiagonal (has mutually perpendicular diagonals),