Eight-Point Circle Theorem


Let ABCD be a quadrilateral with perpendicular polygon diagonals. The midpoints of the sides (a, b, c, and d) 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 a^', b^', c^', and d^'.

See also

Feuerbach's Theorem

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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.

Referenced on Wolfram|Alpha

Eight-Point Circle Theorem

Cite this as:

Weisstein, Eric W. "Eight-Point Circle Theorem." From MathWorld--A Wolfram Web Resource.

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