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
radius
3.5
3.5
diameter
7.0
7.0
circumference
21.99
21.99
area
38.48
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.