Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy
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(Honsberger 1995).
Haruki's Theorem
See also
Circular Triangle, Johnson's Theorem, Venn DiagramExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Haruki's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HarukisTheorem.html