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Haruki's Theorem


HarukisTheorem

Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy

 (ace)/(bdf)=1

(Honsberger 1995).


See also

Circular Triangle, Johnson's Theorem, Venn Diagram

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References

Honsberger, R. "Haruki's Cevian Theorem for Circles." §12.4 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 144-146, 1995.

Referenced on Wolfram|Alpha

Haruki's Theorem

Cite this as:

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

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