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:

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.^[1]^[2]^[3]

The theorem is named after the Japanese mathematician Hiroshi Haruki.

References

^ Wisstein, Eric. "Haruki's Theorem". Wolfram MathWorld. Wolfram MathWorld. Retrieved 19 August 2015.
^ Bogomolny, Alexander. "Cut the Knot". Retrieved 19 August 2015.
^ Ross Honsberger: Episodes in Nineteenth and Twentieth Century Euclidean Geometry. MAA, 1995, p. 144-146

[1] Wisstein, Eric. "Haruki's Theorem". Wolfram MathWorld. Wolfram MathWorld. Retrieved 19 August 2015.

[2] Bogomolny, Alexander. "Cut the Knot". Retrieved 19 August 2015.

[3] Ross Honsberger: Episodes in Nineteenth and Twentieth Century Euclidean Geometry. MAA, 1995, p. 144-146

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