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Chord
From Greek: khorde "gut, string."
A line that links two points on a circle or curve. (pronounced "cord")
Try this Drag either orange dot. The blue line will always remain a chord to the circle.

The blue line in the figure above is called a "chord of the circle c". A chord is a lot like a secant, but where the secant is a line stretching to infinity in both directions, a chord is a line segment that only covers the part inside the circle. A chord that passes through the center of the circle is also a diameter of the circle.

Calculating the length of a chord

Two formulae are given below for the length of the chord,. Choose one based on what you are given to start.

1. Given the radius and central angle

Below is a formula for the length of a chord if you know the radius and central angle. where
r  is the radius of the circle
c  is the angle subtended at the center by the chord
sin  is the sine function (see Trigonometry Overview)

2. Given the radius and distance to center

Below is a formula for the length of a chord if you know the radius and the perpendicular distance from the chord to the circle center. This is a simple application of Pythagoras' Theorem. where
r  is the radius of the circle
d  is the perpendicular distance from the chord to the circle center

Finding the center

The perpendicular bisector of a chord always passes through the center of the circle. In the figure at the top of the page, click "Show Right Bisector". Then move one of the points P,Q around and see that this is always so. This can be used to find the center of a circle: draw one chord and its right bisector. The center must be somewhere along this line. Repeat this and the two bisectors will meet at the center of the circle. See Finding the Center of a Circle in the Constructions chapter for step-by-step instructions.

Intersecting Chords

If two chords of a circle intersect, the intersection creates four line segments that have an interesting relationship. See Intersecting Chord Theorem.

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Other circle topics

General

Equations of a circle

Angles in a circle

Arcs