Eight-Point Circle Theorem

Let be a Quadrilateral with Perpendicular Diagonals. TheMidpoints of the sides (, , , and ) determine a Parallelogram (the VarignonParallelogram) with sides Parallel to the Diagonals. The eight-point circle passesthrough the four Midpoints and the four feet of the Perpendiculars from theopposite 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.

• Hilbert Polynomial
• Hilbert's Axioms
• Hilbert-Schmidt Norm
• Hilbert-Schmidt Theory
• Hilbert's Constants
• Hilbert's Inequality
• Hilbert's Nullstellansatz
• Hilbert Space
• Hilbert's Problems
• Hilbert's Theorem
• Hilbert Transform
• Hillam's Theorem
• Hill Determinant
• Hill's Differential Equation
• Hindu Check
• Hinge
• Hippias' Quadratrix
• Hippopede
• Hi-Q
• Histogram
• Hitch
• Hitting Set
• Hjelmslev's Theorem
• HJLS Algorithm
• HK Integral