First read the conchoid writeup. The conchoid of Nicomedes is the conchoid associated with the data: a line, a point not on the line, and a distance.

If we take the line to be x=a, the point to be (0,0) and the distance to be d then the conchoid has equation:

(x2+y2)(x-a)2=d2x2

Nicomedes used this curve to solve the problem of trisection of the angle, one of the three geometric problems of antiquity some time around 180 BC.

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