Definition:Chord of Contact/Circle

Definition
Let $\CC$ be a circle whose radius is $r$ and whose center is at the origin of a Cartesian plane.

Let $P = \tuple {x_0, y_0}$ be a point which is outside the boundary of $\CC$.

Let $\TT_1$ and $\TT_2$ be a tangents to $\CC$ passing through $P$.

Let:
 * $\TT_1$ touch $\CC$ at $U = \tuple {x_1, y_1}$
 * $\TT_2$ touch $\CC$ at $V = \tuple {x_2, y_2}$

$UV$ is known as the chord of contact on $\CC$ with respect to $P$.

Also see

 * Equation of Chord of Contact on Circle Centered at Origin, demonstrating that $UV$ is the polar of $P$ withy respect to $\CC$.