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Seven Circles Theorem


SevenCirclesTheorem

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite points of tangency are concurrent in a point. The figures above show several possible configurations (Evelyn et al. 1974, pp. 31-37).

SevenCirclesTriangle

Letting the radii of three of the circles approach infinity turns three of the circles into the straight sides of a triangle and the central circle into the triangle's incircle. As illustrated above, the three lines connecting opposite points of tangency (with those along the triangle edges corresponding to the vertices of the contact triangle) concur (Evelyn et al. 1974, pp. 39 and 42).


See also

Circle, Contact Triangle, Hexlet, Incircle, Six Circles Theorem

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References

Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "The Seven Circles Theorem." §3.1 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 31-42, 1974.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 224-225, 1991.

Referenced on Wolfram|Alpha

Seven Circles Theorem

Cite this as:

Weisstein, Eric W. "Seven Circles Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SevenCirclesTheorem.html

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