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

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

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

The size of the angle labelled $$x$$° on this 9-point geoboard is {{}}°.

Find ∠OAB on this 9-point geoboard (in degrees).

Find ∠EFO on this 8-point geoboard (in degrees).

Find ∠DEF on this 8-point geoboard (in degrees).

Find the size of angle $$x$$° (in degrees).

Find the size of angle $$y$$° (in degrees).

The {{}} is a line which intersects the circle exactly once.

The size of the angle labelled $$x$$° is {{}}°.

MY = 8 cm, 
OZ = 13 cm, 
ZM = 12 cm, 
OM = 5 cm.
Find the distance MX.

The size of the angle labelled $$m$$° is {{}}° (in degrees).

The size of the angle labelled $$a$$° is {{}}°.

The angle subtended from arc AB at the circumference of the circle is 11°.  
Find ∠BOA (in degrees).

Starter Quiz

The is a line which intersects the circle exactly once.