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 Resource. https://mathworld.wolfram.com/BrahmaguptasTheorem.html