What Is a Chord?

How a chord is identified

Chords matter because they interact with central angles, intercepted arcs, segment regions, and several circle theorems. A diameter is simply the special case of a chord that passes through the center.

This page keeps the chord and the surrounding arc visible together so you can see that a chord is part of a larger circle relationship, not just an isolated segment drawn inside a disk.

Move one endpoint while keeping the other fixed and the chord changes length. If both endpoints remain on the circle, the segment is still a chord. If the segment reaches the center, it becomes a diameter; if the straight object continues beyond the circle, you are looking at a secant line instead.

• A chord is a segment with both endpoints on the circle.
• A diameter is the longest chord in a given circle because it passes through the center.
• A chord and its intercepted arc share the same endpoints on the circle.
• Chord length depends on how far the chord sits from the center and on the arc it subtends.

Where chords help

• Use chords in problems about intercepted arcs, circle segments, and central angles.
• Use them in theorem work involving equal chords or distances from the center.
• Use them when reading diagrams where a circle contains both straight and curved boundaries.

Chord mix-ups to avoid

• Do not confuse the straight chord with the curved arc that shares its endpoints.
• Do not call a full secant line a chord when the figure extends outside the circle.
• Do not assume every chord is a diameter; only the ones through the center qualify.