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3. Normal and Tangent to a Cassini Oval

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This Demonstration shows Steiner's construction of a tangent on a Cassini oval.

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A Cassini oval is the locus of points such that , where and . If the foci and , then

, .

Let be the intersection of the perpendicular to at and the tangent and let be the intersection of the perpendicular to at and the tangent.

Steiner showed that is the midpoint of the segment .

To construct the tangent at , draw the line through perpendicular to and the line through perpendicular to . Then construct the segment with endpoints on and such that the point is the midpoint of .

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Contributed by: Marko Razpet and Izidor Hafner (August 2018)
Open content licensed under CC BY-NC-SA

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Reference

[1] A. Ostermann and G. Wanner, Geometry by Its History, New York: Springer, 2012.

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