Solved: Circle and radius of curvature Choose a point P on
Chapter 11, Problem 70(choose chapter or problem)
Circle and radius of curvature Choose a point P on a smooth curve C in the plane. The circle of curvature (or osculating circle) at P is the circle that (a) is tangent to C at P, (b) has the same curvature as C at P, and (c) lies on the same side of C as the principal unit normal N (see figure). The radius of curvature is the radius of the circle of curvature. Show that the radius of curvature is 1>k, where k is the curvature of C at P.
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