If the diagonals AC and BD of a cyclic
quadrilateral ABCD are perpendicular, then the midpoints P, Q,
M, N and the feet F, G, H, J of the perpendiculars from the
point of intersection of the diagonals to the sides all lie on a
circle centered at the midpoint of the line EO.
Brahmagupta (598–668) was an Indian
mathematician and astronomer who discovered a neat formula for
the area of a cyclic quadrilateral.
Brahmagupta's Theorem, Area Formula,
Area Formula Extension.