Year 10 - Maths
Identifying which circle theorem to use
Circle theorems
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.
Lesson Summary
You will learn to analyse a circle problem and identify and use an appropriate circle theorem to solve it.
Key Notes
- 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
Vocabulary To Learn
- 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 Mistakes To Avoid
- 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.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
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.
2. Use this key word in a maths sentence and explain it clearly. 'Tangent'
A tangent of a circle is a line that intersects the circle exactly once. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: 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. Correction: 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.
More Lessons In This Unit
- Checking and securing understanding of the parts of a circle Study Guide
- Problem solving with circle theorems Study Guide
- The alternate segment theorem Study Guide
- The angle at the centre of the circle is twice the angle at any point on the circumference Study Guide
- The angle in a semicircle is a right angle Study Guide
- The angles in the same segment are equal Study Guide
- The opposite angles of a cyclic quadrilateral sum to 180° Study Guide
- The perpendicular from the centre of a circle to a chord bisects the chord Study Guide
- The tangent at any point on a circle is perpendicular to the radius at that point Study Guide
- The tangents from an external point are equal in length Study Guide
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