Detailed definition
Understanding Chord
A chord is a line segment with both endpoints on a circle. Unlike an arc, it is straight, and unlike a secant, it does not extend beyond the circle.
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.
Key facts
Important ideas to remember
- 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 it is used
Where chord shows up
- 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.
Common mistakes
What to watch out for
- 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.