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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
    7 主题
  6. Combined-And-Conditional-Probability Aqa Higher
    3 主题
  7. Tree-Diagrams Aqa Higher
    1 主题
  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
    4 主题
  13. Pythagoras-And-Trigonometry Aqa Higher
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  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
    5 主题
  16. Volume-And-Surface-Area Aqa Higher
    3 主题
  17. Circles-Arcs-And-Sectors Aqa Higher
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  18. Area-And-Perimeter Aqa Higher
    4 主题
  19. Circle-Theorems Aqa Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Aqa Higher
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  24. Standard-And-Compound-Units Aqa Higher
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  25. Direct-And-Inverse-Proportion Aqa Higher
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  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
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  28. Sequences Aqa Higher
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  29. Transformations-Of-Graphs Aqa Higher
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  30. Graphing-Inequalities Aqa Higher
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  31. Solving-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
    2 主题
  34. Equation-Of-A-Circle Aqa Higher
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  35. Functions Aqa Higher
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  36. Forming-And-Solving-Equations Aqa Higher
    3 主题
  37. Graphs-Of-Functions Aqa Higher
    6 主题
  38. Linear-Graphs Aqa Higher
    4 主题
  39. Coordinate-Geometry Aqa Higher
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  40. Iteration Aqa Higher
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  41. Simultaneous-Equations Aqa Higher
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  42. Quadratic-Equations Aqa Higher
    4 主题
  43. Linear-Equations Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  45. Rearranging-Formulas Aqa Higher
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  46. Algebraic-Fractions Aqa Higher
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  47. Completing-The-Square Aqa Higher
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  48. Factorising Aqa Higher
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  49. Expanding-Brackets Aqa Higher
    3 主题
  50. Algebraic-Roots-And-Indices Aqa Higher
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  51. Using-A-Calculator Aqa Higher
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  52. Surds Aqa Higher
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  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
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  55. Introduction Aqa Higher
    7 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
    4 主题
  57. Percentages Aqa Higher
    3 主题
  58. Fractions Aqa Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Aqa Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
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  61. Number-Operations Aqa Higher
    10 主题
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Exam code:8300

Circles & chords

What is a chord?

  • A chord is any straight line is a circle that joins any two points on the circumference

    • Chords of equal length are equidistant (the same distance) from the centre

Circle Theorem: The perpendicular bisector of a chord passes through the centre

  • If a line through the centre (such as a radius or diameter) goes through the midpoint of chord

    • it will bisect (cut in half) that chord at right angles to it

A circle with a radius bisecting a chord.

  • To spot this circle theorem on a diagram

    • look for a radius and see if it intersects any chords

    • or look to see if you could draw a radius that bisects a chord

  • When explaining this theorem in an exam you can use either phrase below:

    • A radius bisects a chord at right angles

    • The perpendicular bisector of a chord passes through the centre

Examiner Tips and Tricks

  • Look out for isosceles triangles formed by a chord and two radii

    • Two angles in the triangle will be equal and there will be at least one line of symmetry

Worked Example

The diagram below shows a circle with centre, O.
Two points, P and Q, lie on its circumference.
The radius of the circle is 6 cm.
Angle OPQ = 40º.

Find the length PQ.

A circle of centre, O, has two points on its circumference, P and Q. The lines OQ and PQ are drawn on. The angle OQP = 40º.

Label the radius on the diagram 6 cm

Draw a line from O to the midpoint, M, of the line PQ
The angle formed between the OM and PQ will be a right angle

A diagram showing the same circle with a straight line from the centre to the midpoint of PQ, bisecting it at a right angle.

Use SOHCAHTOA on triangle OMQ to find the length MQ

table row cell cos space 40 end cell equals cell fraction numerator M Q over denominator 6 end fraction end cell row cell 6 space cos space 40 space end cell equals cell space M Q end cell row cell M Q end cell equals cell 4.59626... end cell end table

Double MQ to find the length PQ

<img alt=”4.59626… cross times 2 equals 9.19253…” data-mathml=”<math ><semantics><mrow><mn>4</mn><mo>.</mo><mn>59626</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>&#215;</mo><mn>2</mn><mo>=</mo><mn>9</mn><mo>.</mo><mn>19253</mn><mo>.</mo><mo>.</mo><mo>.</mo></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semanticsg

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