Year 10 - Maths
The tangent at any point on a circle is perpendicular to the radius at that point
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 derive and use the theorem: the tangent at any point on a circle is perpendicular to the radius at that point.
Key Notes
- A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
- Theorems can be thought of as puzzles to solve, you are showing how to find a result
- In order to use this theorem, you may need to draw a diagram or add more information to an existing one
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.
Common Mistakes To Avoid
- Pupils may assume that tangents can be drawn in slightly different directions at the same point on a circle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. Theorems can be thought of as puzzles to solve, you are showing how to find a result.
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 assume that tangents can be drawn in slightly different directions at the same point on a circle. Correction: The tangent at a point on a circle can only be drawn in one possible direction. The tangent is always perpendicular to the radius at that point.
More Lessons In This Unit
- Checking and securing understanding of the parts of a circle Study Guide
- 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 tangents from an external point are equal in length Study Guide
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