Archimedes' Midpoint Theorem

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

Let be the Midpoint of the Arc . Pick at random and pick 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.