Circle or line

Differential Geometry
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Grigorios Kostakos
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Circle or line

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Post by Grigorios Kostakos »

Let \(\overrightarrow{r}(s)\) a natural parametrization of a plane curve. If every tangent line of the curve has the same (constant) distance from a fixed point, prove that the curve must be either a part of a circle, or a part of a line.
Grigorios Kostakos
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