Definition:Chord of Contact/Circle

Definition

Let $\CC$ be a circle embedded in the plane.

Let $P$ be a point also embedded in the plane 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 $U$

$\TT_2$ touch $\CC$ at $V$.

$UV$ 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 $\CC$.

• Results about chords of contact can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $4$. Pole and polar
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): chord
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): chord