Definition:Center of Curvature

Definition
Let $C$ be a curve embedded in the plane.

Let $N$ be the normal to $C$ at a point $P$.

Let $\rho$ be the radius of curvature of $C$ at $P$.

Let $Q$ be the point on $N$ which is at a distance $\rho$ from $P$ on the concave side of $C$.

$Q$ is known as the center of curvature of $C$ at $P$.