3.2.4

Circle Theorems - Perpendicular Bisector

Test yourself

Circle Theorems

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Perpendicular bisector goes through centre

  • The perpendicular bisector of a chord always goes through the centre of the circle.
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Proof

  • Draw the perpendicular from centre, O, to the chord AB.
  • Draw a radius to A and another to B to form two triangles.
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Proof continued

  • Their hypotenuses are the same length (because they are both radii) and they share another edge so the triangles are congruent by the ‘RHS’ rule.
  • Therefore AM = BM and so the perpendicular splits the chord exactly in half.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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