In a cyclic quadrilateral having perpendicular diagonals , the perpendiculars to the sides through point of intersection of the diagonals (the anticenter) always bisects the opposite side (so , , , and are the midpoints of the corresponding sides of the quadrilateral).
Brahmagupta's Theorem
See also
Anticenter, Cyclic Quadrilateral, MidpointExplore with Wolfram|Alpha
References
Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., p. 37, 1995.Referenced on Wolfram|Alpha
Brahmagupta's TheoremCite this as:
Weisstein, Eric W. "Brahmagupta's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrahmaguptasTheorem.html