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Archimedes' Midpoint Theorem

\begin{figure}\begin{center}\BoxedEPSF{ArchimedesMidpointTheorem.epsf}\end{center}\end{figure}

Let $M$ be the Midpoint of the Arc $AMB$. Pick $C$ at random and pick $D$ such that $MD\perp AC$ (where $\perp$ denotes Perpendicular). Then

\begin{displaymath}
AD=DC+BC.
\end{displaymath}

See also Midpoint


References

Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 31-32, 1991.




© 1996-9 Eric W. Weisstein
1999-05-25