Parts of a circle, chords and tangents

Circle questions use exact vocabulary and three facts about chords and tangents, usually with Pythagoras.

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Vocabulary

Radius: centre to edge. Diameter: edge to edge through the centre.
Chord: a straight line joining two points on the circle.
Tangent: a straight line touching the circle at one point.
Arc: part of the circumference. Sector: a slice between two radii.
Segment: the region between a chord and an arc.
O diameter sector radius arc chord segment tangent
Parts of a circle.

Three facts

1. A tangent is perpendicular to the radius at the point where it touches.
2. The two tangents from a point outside a circle are equal in length.
3. The perpendicular from the centre to a chord bisects the chord (and the line from the centre to the midpoint of a chord is perpendicular to it).

Using Pythagoras

Radius 13 cm, chord 24 cm. Half the chord is 12 cm.
The distance from the centre to the chord is √(132 − 122) = 5 cm.
Tangent from P where OP = 10 cm and the radius is 6 cm: the tangent length is √(102 − 62) = 8 cm.
O 13 cm 5 cm 12 cm 12 cm chord 24 cm
The perpendicular from the centre bisects the chord: √(13² − 12²) = 5 cm.
Worked example

A circle has radius 13 cm. A chord is 24 cm long. How far is the chord from the centre?

  1. The perpendicular from the centre bisects the chord: half is 12 cm.
  2. √(132 − 122) = √25 = 5

Answer: 5 cm

Key idea

Tangent ⟂ radius. Tangents from a point are equal. The perpendicular from the centre bisects a chord. Then use Pythagoras.

Key words
Radius
The distance from the centre of a circle to its edge.
Chord
A straight line joining two points on a circle.
Arc
Part of the circumference of a circle.
Sector
The region of a circle between two radii and an arc, like a slice of pizza.
Segment
The region of a circle between a chord and an arc.

All GCSE and International GCSE Mathematics key terms and definitions →

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Extra practice

2 more questions

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  1. A circle has radius 25 cm and a chord of 14 cm. How far is the chord from the centre?

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    Answer: 24 cm

    Half the chord is 7. √(252 − 72) = 24 cm.

  2. O is the centre of a circle of radius 8 cm. P is 17 cm from O. Find the length of the tangent from P to the circle.

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    Answer: 15 cm

    The tangent meets the radius at 90°: √(172 − 82) = 15 cm.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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