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Clairaut's Angle Trisection

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This Demonstration shows Clairaut's angle trisection, which uses a hyperbola.

Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA

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Let be the given angle with and on the circle with center . Let the points and trisect the segment and let the bisector of the angle cut at and the circle at . Then . Let the hyperbola with focus , vertex , and directrix cut the circle at point . Let be the orthogonal projection of on and let be the point symmetrical to relative to . Then .

Reference

[1] W. W. Rouse Ball, H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 346.

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