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# Trisecting an Angle Using the Cycloid of Ceva

The cycloid of Ceva has the polar equation . To trisect the angle , construct a line parallel to the polar axis (the positive axis). Let be the point of intersection of the cycloid and the line. Then the angle is one-third of the angle . Proof: let angle be and let the point on the axis be such that . Let be the orthogonal projection of on the line . The angle , so . Since , , . So angle equals , but .

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Reference
[1] J. Loy. "Trisection of an Angle." (1997/2003) www.cerebral-palsy.net/trisectangle/trisectangle.html.

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