Chord

Dependencies: Circle, Segment. A derived definition: choose two points on a circle and join them with a segment.

Definition

Let $A$ and $B$ be points on circle $\odot O$.

The segment $AB$ is called a chord of the circle.

A chord is the straight connection between two points of a circle. It lies inside the circle with both endpoints on the circle, and it links many important circle concepts: distance from the center, the corresponding arc, and inscribed angles.

Remarks

• A diameter is the longest chord. Chords get longer as they approach the center. A chord through the center is a diameter, with length twice the radius. No chord is longer than a diameter.
• A chord divides a circle into two arcs. These are the minor and major arcs. Equal chords subtend equal arcs.
• Perpendicular chord theorem. A perpendicular from the center to a chord meets it at its midpoint and also bisects its arcs (Diameter through chord midpoint ⊥ chord).
• Distance from center to chord. In a fixed circle, a longer chord has a smaller perpendicular distance from the center.