Tangent to a Cycloid

The cycloid is the locus of a point on a circle rolling along a straight line. This Demonstration illustrates a theorem proved by Descartes: the tangent to the cycloid at a point is perpendicular to , where is the point of contact of the circle and the line.

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Reference
[1] University of St Andrews Scotland, School of Mathematics and Statistics. The MacTutor History of Mathematics archive. "Cycloid." (Nov 29, 2012) www-history.mcs.st-and.ac.uk/Curves/Cycloid.html.
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