Identifying which circle theorem to use | Maths | Quizalize & Oak National Academy

Starter quiz

∠AKC = 21° ∠AWK is subtended by the chord AK. $a$ ° = ______°.

'21' ✓
The image shows a circle, a tangent to the circle and three line segments forming a triangle inside the circle. The size of the angle labelled $b$ ° is ______°.

'56' ✓
Find the size of angle $c$ ° (in degrees).

'69' ✓
The size of angle $d$ ° is ______°.

'124' ✓
The size of angle $e$ ° is ______° .

'57' ✓
Calculate the size of angle $g$ ° (in degrees).

28.5°

33°

114° ✓

147°

Not enough information

Exit quiz

Points X and Y are points where two separate tangents intersect the circle. $a$ ° = ______°.

'222' ✓
Points X and Y are points where two separate tangents intersect the circle. Calculate the size of the angle labelled $b$ °.

42°

48°

69° ✓

111°

Not enough information.
Points A and B are points where two separate tangents intersect the circle. Calculate the size of the angle labelled $c$ °.

38°

41°

45°

49° ✓

Not enough information.
Points A and B are points where two separate tangents intersect the circle. $d$ ° = ______°.

'35' ✓
The tangent shown intersects the circle at point T. $x$ ° = ______°.

'48' ✓
Point T is a point on the circumference where a tangent intersects the circle. $y$ ° = ______°.

'77' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

There are many circle theorems so it is important to be clear about each one
Extra lines can be added to a diagram to help determine which theorem to use
Some problems require the use of more than one theorem

Common misconception

Pupils may conflate cyclic quadrilaterals with cases of "the angle at the centre of a circle is twice the angle at the circumference" theorem, when the angle at the centre is a reflex angle.

While the two diagrams may look similar at a glance, pay extra attention to whether all four points of the quadrilateral are on the circumference or if one of the points is in the centre.

Keywords

Tangent - A tangent of a circle is a line that intersects the circle exactly once.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Perpendicular - Two lines are perpendicular if they meet at right angles.
Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.