Definition:Power of Point with respect to Circle

Definition
Let $\CC$ be a circle embedded in the Cartesian plane with its center located at the origin.

Let $\CC$ have radius $r$.

Let $P = \tuple {x, y}$ be a point in the plane of $\CC$.

The power of $P$ with respect to $\CC$ is the quantity:
 * $x^2 + y^2 - r^2$

Also see

 * Length of Tangent from Point to Circle center Origin, which applies when $P$ is outside $\CC$


 * Tangent Secant Theorem