4.5.7

Alternate Segment Theorem

Test yourself

Circle Theorems

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Alternate segment theorem

  • The angle between a tangent and a chord is always equal to the angle at the circumference of any triangle formed from the chord.
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Proof

  • Draw in a diameter from the point where the tangent touches. Connect it to the other end of the chord.
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Proof continued

  • Using ‘radius and tangent meet at a right angle’ we get a right angle where the diameter meets the tangent.
  • Using ‘angle in a semicircle is 90°’ we get that the angle at the other end of the chord is a right angle too.
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Proof continued

  • We find that the angle at the bottom of the diameter is the same as x.
  • Using ‘angles in same segment’ we get that x = y.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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