Inscribed quadrilateral with perpendicular diagonals

An inscribed quadrilateral is a quadrilateral whose vertices all lie on a circle (it is cyclic). If the diagonals of such a quadrilateral are perpendicular, interesting geometric properties arise. For example, the areas of the triangles formed by the intersection point of the diagonals and the vertices have special relationships.

Important properties

• The intersection point of the diagonals is inside the circle.

• The product of the lengths of the diagonals equals the sum of the products of the pairs of opposite sides: $AC \cdot BD = AB \cdot CD + BC \cdot DA$ (Brahmagupta's formula for perpendicular diagonals).

• The perpendicular diagonals divide the quadrilateral into four right triangles.