Math Playground
Geometry

Chord

Any straight line connecting two points on a circle.

A chord is a straight line joining two points on a circle. Slide its endpoints around and the chord grows and shrinks — the biggest one possible passes through the centre, and that's the diameter.

Stretch the radius
r
radius
3.5
diameter
7.0
circumference
21.99
area
38.48

Chord facts worth knowing

  • The diameter is the longest chord — every other chord is shorter.
  • A line from the centre perpendicular to a chord bisects it (cuts it exactly in half).
  • Equal chords are the same distance from the centre — and vice versa.
  • Two chords that meet inside a circle split each other so that the products of the pieces are equal: a·b = c·d (the *intersecting chords* theorem).
Your turn

A chord is 16 cm long. The perpendicular from the centre meets it — how long is each half, and what does that perpendicular do?

A chord and an arc together cut off a segment of the circle; a chord plus the two radii to its ends cuts off a triangle. Drag the chord above and slide the angle to see the slice change.