Haruki's Theorem

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:

${\displaystyle s_{1}\cdot s_{3}\cdot s_{5}=s_{2}\cdot s_{4}\cdot s_{6}}$

Illustration of Haruki's Theorem:
${\displaystyle {\frac {s_{1}}{s_{2}}}\cdot {\frac {s_{3}}{s_{4}}}\cdot {\frac {s_{5}}{s_{6}}}=1}$

where ${\displaystyle s_{1},s_{2},s_{3},s_{4},s_{5},s_{6}}$ are the measure of segments connecting the inner and outer intersection points.^[1][2][3][4]

The theorem is named after the Japanese mathematician Hiroshi Haruki.