# 2. Normal and Tangent to a Cassini Oval

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This Demonstration shows how to construct the normal and tangent to a Cassini oval at a point .

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Contributed by: Marko Razpet and Izidor Hafner (August 2018)

Open content licensed under CC BY-NC-SA

## Details

Let , let be the angle between and the normal to the oval at , and let be the angle between the normal and . We must prove that and .

Since is an external angle of the triangle , . Suppose .

Using the Steiner formula

,

(.

On the other hand, by the tangent law for the triangle ,

.

Since

Thus and .

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