I'm trying out some exercises in differential geoemtry and came accross this one:(adsbygoogle = window.adsbygoogle || []).push({});

If [tex]\gamma(t)[/tex] is unit-speed, and that all its normals pass through a given point, show that the trace of [tex]\gamma(t)[/tex] is part of a circle.

My solution so far:

Let a be a point where all the normals pass, then we know that [tex]\gamma(t) - a = s(t) N(t) \ \forall t[/tex], where s(t) is a real-valued function.

But where should I take it from there? All I know is that ultimately I want to show that |s(t)| is constant for all t.

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# Showing that some curve is a circle

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