Haruki's Theorem

Short description: Geometry Theorem

Illustration of Haruki's Theorem:
[math]\displaystyle{ \frac{s_1}{s_2} \cdot \frac{s_3}{s_4} \cdot \frac{s_5}{s_6} = 1 }[/math]

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:

[math]\displaystyle{ s_1 \cdot s_3 \cdot s_5 = s_2 \cdot s_4 \cdot s_6 }[/math]

where [math]\displaystyle{ s_1, s_2, s_3, s_4, s_5, s_6 }[/math] are the measure of segments connecting the inner and outer intersection points.

The theorem is named after the Japanese mathematician Hiroshi Haruki.