A tangent of a circle is a line that intersects the circle exactly once.

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

Two lines are perpendicular if they meet at right angles.

Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

The tangents from an external point are equal in length

Maths

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.

Circle theorems

A triangle is formed on the circle from a segment of a tangent, a radius and another line segment. The size of angle $$a$$° is {{}}°.

Points T and U are points where two separate tangents intersect the circle.
Find the size of angle $$b$$° (in degrees).

Points G and H are points where two separate tangents intersect the circle.
The size of angle $$c$$° is {{}}°.

Points Q and P are points where two separate tangents intersect the circle.
The size of the angle labelled $$d$$° is {{}}°.

Points J and K are points where two separate tangents intersect the circle.
The size of angle $$e$$° is {{}}°.

Points L and N are points where two separate tangents intersect the circle. ∠LMN = 118°.
$$g$$° = {{}}°.

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

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

∠ATC = 51°
∠ABT is subtended by the chord AT.
The size of the angle labelled $$e$$° is {{}}°.

∠PEF is subtended by the chord PF.
∠PFE is subtended by the chord PE.
Find ∠EPD (in degrees).

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

This lesson will be removed by end of Summer Term 2025.

The tangents from an external point are equal in length

Lesson outcome

This lesson will be removed by end of Summer Term 2025.