Brahmagupta's Theorem


In a cyclic quadrilateral ABCD having perpendicular diagonals AC_|_BD, the perpendiculars to the sides through point T of intersection of the diagonals (the anticenter) always bisects the opposite side (so M_(AB), M_(BC), M_(CD), and M_(DA) are the midpoints of the corresponding sides of the quadrilateral).

See also

Anticenter, Cyclic Quadrilateral, Midpoint

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Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., p. 37, 1995.

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Brahmagupta's Theorem

Cite this as:

Weisstein, Eric W. "Brahmagupta's Theorem." From MathWorld--A Wolfram Web Resource.

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