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

Maths

Checking and securing understanding of the parts of a circle

The angle at the centre of the circle is twice the angle at any point on the circumference

The angle in a semicircle is a right angle

The tangent at any point on a circle is perpendicular to the radius at that point

The angles in the same segment are equal

The alternate segment theorem

The opposite angles of a cyclic quadrilateral sum to 180°

The tangents from an external point are equal in length

Identifying which circle theorem to use

Problem solving with circle theorems

In the prior unit, pupils applied their understanding of angles to solve increasingly complex problems. In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

Circle theorems

On this 10-point geoboard ∠AOM is {{}}°.

On this 10-point geoboard  ∠OAM is {{}}°.

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

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

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.).

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

The size of the angle subtended by the chord AC is {{}}°?

The image shows an 8-point geoboard. The size of angle $$b$$° is {{}}°.

On this 8-point geoboard the size of the angle labelled $$c$$° is {{}}°.

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

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

Lesson outcome