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 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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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