Definition:Power of Point/Cartesian

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
• Power of a Point Theorem

• Results about the power of a point can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $11$. Geometrical meaning of the expression $x^2 + y^2 - r^2$