Haruki's Theorem

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

x ⋅ y ⋅ z = a ⋅ b ⋅ c

where x , y , z , a , b , c are the measure of segments connecting the inner and outer interesection points