New
New
Year 10
Higher

Problem solving with circle theorems

I can use my knowledge of circle theorems to solve problems.

New
New
Year 10
Higher

Problem solving with circle theorems

I can use my knowledge of circle theorems to solve problems.

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Lesson details

Key learning points

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

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.

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.

For some questions, different combinations of circle theorems can be applied to solve the problem. Encourage pupils to write down which circle theorem they are using at each stage of their solution and discuss the efficiency of alternate solutions.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
$$a$$° = °.
An image in a quiz
Correct Answer: 54, 54°, 54 degrees
Q2.
Calculate the size of angle $$b$$°.
An image in a quiz
27°
36°
54°
Correct answer: 108°
126°
Q3.
The diagram shows a circle with a tangent and three line segments that form a triangle inside the triangle. $$c$$° = °.
An image in a quiz
Correct Answer: 108, 108°, 108 degrees
Q4.
$$d$$° = °.
An image in a quiz
Correct Answer: 96, 96°, 96 degrees
Q5.
Points A and B are points where two separate tangents intersect the circle. $$c$$° = °.
An image in a quiz
Correct Answer: 47, 47°, 47 degrees
Q6.
Points A and B are points where two separate tangents intersect the circle. Find the size of angle $$d$$°.
An image in a quiz
Correct answer: 38°
42°
43°
47°

6 Questions

Q1.
The length of chord MN is cm (2 d.p.).
An image in a quiz
Correct Answer: 29.66, 29.66 cm
Q2.
$$a$$° = ° (2 d.p.).
An image in a quiz
Correct Answer: 67.98, 67.98 degrees, 67.98°
Q3.
$$u = 7k + 4$$. $$v = 9k$$. $$u$$° = °.
An image in a quiz
Correct Answer: 81, 81°, 81 degrees
Q4.
$$m + k = 207$$. $$k$$° = °.
An image in a quiz
Correct Answer: 138, 138°, 138 degrees
Q5.
The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $$b : c : d = 5 : 7 : 6$$. $$e$$° = °.
An image in a quiz
Correct Answer: 35, 35°, 35 degrees
Q6.
The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $$b : c : d = 5 : 7 : 6$$. $$g : h = 14 : 9$$. $$h$$° = °.
An image in a quiz
Correct Answer: 63, 63°, 63 degrees