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Haruki's Theorem says that given three intersecting circles that only intersect each other at two points that the lines connecting the inner intersecting points to the outer satisfy:

\( {\displaystyle x\cdot y\cdot z=a\cdot b\cdot c} \)

Illustration for Haruki's Theorem

Illustration of Haruki's Theorem

where \( {\displaystyle x,y,z,a,b,c} \) are the measure of segments connecting the inner and outer intersection points

[1] [2]
References

Wisstein, Eric. "Haruki's Theorem". Wolfram MathWorld. Wolfram MathWorld. Retrieved 19 August 2015.
Bogomolny, Alexander. "Cut the Knot". Retrieved 19 August 2015.

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