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 .

**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

1999-05-25