## Eight-Point Circle Theorem

Let be a Quadrilateral with Perpendicular Diagonals. The Midpoints of the sides (, , , and ) determine a Parallelogram (the Varignon Parallelogram) with sides Parallel to the Diagonals. The eight-point circle passes through the four Midpoints and the four feet of the Perpendiculars from the opposite sides , , , and .

See also Feuerbach's Theorem

References

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.

© 1996-9 Eric W. Weisstein
1999-05-25