4.5.5

Tangent Lengths

Test yourself

Circle Theorems

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Lengths of tangents

  • Two tangents to the same circle from the same point (C) will be the same length.
    • Here AC = BC
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Proof

  • Add radii from the points, A and B, where the tangents touch and draw a line from the centre of the circle, O to where the tangents meet, C.
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Proof continued

  • These are congruent triangles (by using the 'RHS' rule).
  • They share a common side (length x) and another side which is a radius.
  • Therefore the remaining side, the tangent, is the same length for both.

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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