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Year 10
Higher

The perpendicular from the centre of a circle to a chord bisects the chord

I can derive and use the theorem: the perpendicular from the centre of a circle to a chord bisects the chord.

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New
New
Year 10
Higher

The perpendicular from the centre of a circle to a chord bisects the chord

I can derive and use the theorem: the perpendicular from the centre of a circle to a chord bisects the chord.

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Lesson details

Key learning points

  1. A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
  2. Theorems can be thought of as puzzles to solve, you are showing how to find a result
  3. In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Keywords

  • Bisect - To bisect means to cut or divide an object into two equal parts.

  • Chord - A chord is any line segment joining two points on the circumference of a circle.

Common misconception

Pupils may assume that a radius which intersects a chord always bisects the chord.

A radius only bisects a chord if they are perpendicular.


To help you plan your year 10 maths lesson on: The perpendicular from the centre of a circle to a chord bisects the chord, download all teaching resources for free and adapt to suit your pupils' needs...

The lesson demonstrates how this circle theorem could be explored practically by using a pair of compasses, using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.
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equipment-required

Equipment

Ruler, protractor, pair of compasses, pencil

copyright

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Which of these statements are correct?
A chord can be a radius.
Correct answer: A chord can be a diameter.
A chord can be a tangent.
Correct answer: A segment can be a sector.
A minor sector can be a segment.
Q2.
Find the size of angle $$a$$°.
An image in a quiz
30°
60°
Correct answer: 90°
120°
Not enough information.
Q3.
The size of the angle subtended by the chord AC is °?
An image in a quiz
Correct Answer: 24, 24°, 24 degrees, 24degrees
Q4.
The image shows an 8-point geoboard. The size of angle $$b$$° is °.
An image in a quiz
Correct Answer: 22.5, 22.5°, 22.5 degrees
Q5.
On this 8-point geoboard the size of the angle labelled $$c$$° is °.
An image in a quiz
Correct Answer: 67.5, 67.5°, 67.5 degrees, 67.5degrees
Q6.
The area of triangle ABC is 336 cm². Find the area of the circle, in cm² (3 s.f.)
An image in a quiz
25
48
50
625
Correct answer: 1960

6 Questions

Q1.
On this 10-point geoboard ∠AOM is °.
An image in a quiz
Correct Answer: 72, 72°, 72 degrees
Q2.
On this 10-point geoboard ∠OAM is °.
An image in a quiz
Correct Answer: 18, 18°, 18 degrees
Q3.
Find ∠OMA on this 10-point geoboard (in degrees).
An image in a quiz
Correct Answer: 90, 90°, 90 degrees
Q4.
BMA and OMC are straight line segments. AM = 10 cm Which of these are also 10 cm long?
An image in a quiz
Line segment OB
Line segment OC
Line segment OM
Correct answer: Line segment BM
Line segment CM
Q5.
BMA and OMC are straight line segments. AM = 10 cm. Radius OB has length 14 cm. Find the length of OM (in cm, to 2 d.p.).
An image in a quiz
Correct Answer: 9.80, 9.80 cm
Q6.
BMA and OMC are straight line segments. AM = 10 cm. Radius OB has length 14 cm. The size of ∠MOB is ° (1.d.p.).
An image in a quiz
Correct Answer: 45.6, 45.6°, 45.6 degrees, 45.6degrees