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Four Conics Theorem

FourConicsTheorem

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn et al. 1974, pp. 23 and 25).

FourConicsDual

The dual theorem states that if two common tangents of each pair of three conics touch a fourth conic, then the remaining common tangents of each pair intersect in three collinear points (Evelyn et al. 1974, pp. 24-25).

See also

Conic Section, Three Conics Theorem

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References

Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "The Four-Conics Theorem." §2.4 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 22-29, 1974.

Referenced on Wolfram|Alpha

Four Conics Theorem

Cite this as:

Weisstein, Eric W. "Four Conics Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FourConicsTheorem.html

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