Let be a quadrilateral with perpendicular polygon diagonals. The midpoints of the sides (, , , and ) determine a parallelogram (the Varignon parallelogram) with sides parallel to the polygon diagonals. The eight-point circle passes through the four midpoints and the four feet of the perpendiculars from the opposite sides , , , and .

Brand, L. "The Eight-Point Circle and the Nine-Point Circle." Amer. Math. Monthly 51, 84-85, 1944.

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 11-13, 1976.

CITE THIS AS:

Weisstein, Eric W. "Eight-Point Circle Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Eight-PointCircleTheorem.html