Year 10 - Maths
Checking and securing understanding of the parts of a circle
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 identify the parts of a circle, including finding the area and perimeter of a sector.
Key Notes
- A chord splits the circle into two uneven pieces
- The smaller piece is the minor segment and the larger is the major segment
- Using fractions, you can calculate the area of a sector of a circle and you can calculate the curved length of a sector
- To find the perimeter, you will need to add the radius twice
- An exact answer may be given in terms of π
Vocabulary To Learn
- Subtended: An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.
Common Mistakes To Avoid
- Pupils may think that every line segment that touches a circle exactly once is a tangent (even when it is not perpendicular to the radius at that point).
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A chord splits the circle into two uneven pieces. The smaller piece is the minor segment and the larger is the major segment.
2. Use this key word in a maths sentence and explain it clearly. 'Subtended'
An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve. 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 think that every line segment that touches a circle exactly once is a tangent (even when it is not perpendicular to the radius at that point). Correction: If unsure, try extending the line segment to beyond the edges of the circle to check whether it would intersect the circle again.
More Lessons In This Unit
- Identifying which circle theorem to use 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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