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

Starter quiz

Which of these statements are correct?

A chord can be a radius.

A chord can be a diameter. ✓

A chord can be a tangent.

A segment can be a sector. ✓

A minor sector can be a segment.
Find the size of angle $a$ °.

30°

60°

90° ✓

120°

Not enough information.
The size of the angle subtended by the chord AC is ______°?

'24' ✓
The image shows an 8-point geoboard. The size of angle $b$ ° is ______°.

'22.5' ✓
On this 8-point geoboard the size of the angle labelled $c$ ° is ______°.

'67.5' ✓
The area of triangle ABC is 336 cm². Find the area of the circle, in cm² (3 s.f.)

25

48

50

625

1960 ✓

On this 10-point geoboard ∠AOM is ______°.

'72' ✓
On this 10-point geoboard ∠OAM is ______°.

'18' ✓
Find ∠OMA on this 10-point geoboard (in degrees).

'90' ✓
BMA and OMC are straight line segments. AM = 10 cm Which of these are also 10 cm long?

Line segment OB

Line segment OC

Line segment OM

Line segment BM ✓

Line segment CM
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.).

'9.80' ✓
BMA and OMC are straight line segments. AM = 10 cm. Radius OB has length 14 cm. The size of ∠MOB is ______° (1.d.p.).

'45.6' ✓

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

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

A radius only bisects a chord if they are perpendicular.

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.