Brahmagupta’s theorem

Brahmagupta’s theorem states that AF =FD.

Brahmagupta continues,

12.23. The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular [altitudes].^[11]

So, in a “non-unequal” cyclic quadrilateral (that is, an isosceles trapezoid), the length of each diagonal is .

He continues to give formulas for the lengths and areas of geometric figures, such as the circumradius of an isosceles trapezoid and a scalene quadrilateral, and the lengths of diagonals in a scalene cyclic quadrilateral. This leads up to Brahmagupta’s famous theorem