Definition:Power of Point
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Definition
Let $C$ be a circle in the the plane whose center is $O$ and whose radius is $r$.
Let $P$ be a point whose distance from $O$ is $d$.
The power of $P$ with respect to $C$ is defined to be:
- $d^2 - r^2$
Cartesian Embedding
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
- Results about the power of a point can be found here.
Sources
- 1967: H.S.M. Coxeter and S.L. Greitzer: Geometry Revisited: Chapter $2$ : "Some Properties of Circles."