Brahmagupta formula for cyclic quadrilaterals in the hyperbolic plane

The Heron formula relates the area of an Euclidean triangle to its side lengths. Indian mathematician and astronomer Brahmagupta, in the seventh century, gave the analogous formulas for a convex cyclic quadrilateral. Several non-Euclidean versions of the Heron theorem have been known for a long time.
In this paper we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of an equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmahupta formula for such quadrilaterals.