Definition:Chord

This page has been identified as a candidate for refactoring of basic complexity. In particular: Make the general version the top version, with the various other definitions as subspecialisations Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code.

Definition

Chord of a Circle

A chord of a circle is a straight line segment whose endpoints are on the circumference of the circle.

In the diagram above, the lines $CD$ and $EF$ are both chords.

Chord of an Ellipse

 

A chord of an ellipse is a straight line segment whose endpoints are on the perimeter of the ellipse.

In the diagram above, the line $AB$ is a chord.

Chord of a Polygon

A chord of a polygon $P$ is a straight line connecting two non-adjacent vertices of $P$:

In the above diagram, $DF$ is a chord of polygon $ABCDEFG$.

Chord of a Parabola

 

A chord of a parabola is a straight line segment whose endpoints are on the parabola.

In the diagram above, the lines $AB$ and $C$ are chords.

Chord of a general Curve

Let $\CC$ be a curve.

A chord of $\CC$ is a straight line segment whose endpoints lie on $\CC$.

Hence it is a segment of a secant line $\LL$ between the points of intersection of $\CC$ with $\LL$.

Circle

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 $P$.

Ellipse

Let $\EE$ be an ellipse embedded in the plane.

Let $P$ be a point also embedded in the plane which is outside the boundary of $\EE$.

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

Let:

$\TT_1$ touch $\EE$ at $U$

$\TT_2$ touch $\EE$ at $V$.

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

Also see

• Results about chords can be found here.