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It is a straight line!

Differential Geometry
Tsakanikas Nickos
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It is a straight line!

Let $c \ \colon \left[ 0,1 \right] \longrightarrow \mathbb{R}^{n}$ be a regular parametrized curve with the property that all its tangents pass through a fixed point. Show that the image of $c$ lies in a straight line. What can be said if the condition of regularity is dropped?