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Archimedes' Midpoint Theorem

ArchimedesMidpointTheorem

Archimedes' midpoint theorem states that if M is the midpoint of the arc AMB, C is a point on this arc with AC>BC, and D lies on AC with MD perpendicular to AC, then

AD=DC+BC.

See also

Midpoint

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References

Bogomolny, A. "The Broken Chord Theorem." https://cut-the-knot.org/Curriculum/Geometry/BrokenChord.shtml.Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 31-32, 1991.Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 1-2, 1995.

Referenced on Wolfram|Alpha

Archimedes' Midpoint Theorem

Cite this as:

Weisstein, Eric W. "Archimedes' Midpoint Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ArchimedesMidpointTheorem.html

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