Problem solving with circle theorems | Maths | Quizalize & Oak National Academy

Starter quiz

$a$ ° = ______°.

'54' ✓
Calculate the size of angle $b$ °.

27°

36°

54°

108° ✓

126°
The diagram shows a circle with a tangent and three line segments that form a triangle inside the triangle. $c$ ° = ______°.

'108' ✓
$d$ ° = ______°.

'96' ✓
Points A and B are points where two separate tangents intersect the circle. $c$ ° = ______°.

'47' ✓
Points A and B are points where two separate tangents intersect the circle. Find the size of angle $d$ °.

9°

38° ✓

42°

43°

47°

Exit quiz

The length of chord MN is ______ cm (2 d.p.).

'29.66' ✓
$a$ ° = ______° (2 d.p.).

'67.98' ✓
$u = 7k + 4$ . $v = 9k$ . $u$ ° = ______°.

'81' ✓
$m + k = 207$ . $k$ ° = ______°.

'138' ✓
The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $b : c : d = 5 : 7 : 6$ . $e$ ° = ______°.

'35' ✓
The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $b : c : d = 5 : 7 : 6$ . $g : h = 14 : 9$ . $h$ ° = ______°.

'63' ✓

Worksheet

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Lesson Details

Key learning points

Circle theorems can be used in situations involving circles
It is not always obvious that a circle theorem can be used
Sometimes you may wish to add more to a diagram in order to deduce more information

Common misconception

Pupils may not recognise or confuse which circle theorems to apply in a multi-step problem.

Encourage pupils to add more to a diagram in order to deduce more information about the problem. Drawing an additional line segment, such chord or radius may a useful first step.

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.