Taking the locus of midpoints from a fixed point to a circle of radius 
results in a circle of radius 
. This follows trivially from
 |  | ![[-x; 0]+1/2([rcostheta; rsintheta]-[-x; 0])](/images/equations/Circle-PointMidpointTheorem/Inline5.svg) |
(1)
|
 |  | ![[1/2rcostheta-1/2x; 1/2sintheta].](/images/equations/Circle-PointMidpointTheorem/Inline8.svg) |
(2)
|
Circle-Point Midpoint Theorem
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References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 17, 1929.Referenced on Wolfram|Alpha
Circle-Point Midpoint TheoremCite this as:
Weisstein, Eric W. "Circle-Point Midpoint Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Circle-PointMidpointTheorem.html