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Euler's Distribution Theorem

For signed distances on a line segment,

AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0,

since

(b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

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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. 3, 1929.

Referenced on Wolfram|Alpha

Euler's Distribution Theorem

Cite this as:

Weisstein, Eric W. "Euler's Distribution Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulersDistributionTheorem.html

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