Haruki's Theorem

Illustration of Haruki's Theorem:
$\frac{s_1}{s_2}\cdot \frac{s_3}{s_4}\cdot \frac{s_5}{s_6}=1$

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:

$s_1\cdot s_3\cdot s_5=s_2\cdot s_4\cdot s_6$

where $s_1,s_2,s_3,s_4,s_5,s_6$ are the measure of segments connecting the inner and outer intersection points.

The theorem is named after the Japanese mathematician Hiroshi Haruki.