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Circle-Point Midpoint Theorem

\begin{figure}\begin{center}\BoxedEPSF{CirclePointMidpointTheorem.epsf scaled 700}\end{center}\end{figure}

Taking the locus of Midpoints from a fixed point to a circle of radius $r$ results in a circle of radius $r/2$. This follows trivially from

{\bf r}(\theta)&=&\left[\begin{array}{c}-x\\ 0\end{array}\rig...
...\over 2}}x\\ {\textstyle{1\over 2}}\sin\theta\end{array}\right].


Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 17, 1929.

© 1996-9 Eric W. Weisstein