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Maths Gcse Edexcel Higher

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  1. Scatter-Graphs-And-Correlation Edexcel Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Edexcel Higher
    4 主题
  3. Histograms Edexcel Higher
    3 主题
  4. Statistical-Diagrams Edexcel Higher
    7 主题
  5. Averages-Ranges-And-Data Edexcel Higher
    8 主题
  6. Combined-And-Conditional-Probability Edexcel Higher
    3 主题
  7. Tree-Diagrams Edexcel Higher
    1 主题
  8. Simple-Probability-Diagrams Edexcel Higher
    3 主题
  9. Transformations Edexcel Higher
    5 主题
  10. Vectors Edexcel Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Edexcel Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Edexcel Higher
    4 主题
  13. Pythagoras-And-Trigonometry Edexcel Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Edexcel Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Edexcel Higher
    5 主题
  16. Volume-And-Surface-Area Edexcel Higher
    3 主题
  17. Circles-Arcs-And-Sectors Edexcel Higher
    2 主题
  18. Area-And-Perimeter Edexcel Higher
    4 主题
  19. Circle-Theorems Edexcel Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Edexcel Higher
    3 主题
  22. Symmetry-And-Shapes Edexcel Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Edexcel Higher
    2 主题
  24. Standard-And-Compound-Units Edexcel Higher
    5 主题
  25. Direct-And-Inverse-Proportion Edexcel Higher
    2 主题
  26. Problem-Solving-With-Ratios Edexcel Higher
    2 主题
  27. Ratios Edexcel Higher
    3 主题
  28. Sequences Edexcel Higher
    4 主题
  29. Transformations-Of-Graphs Edexcel Higher
    2 主题
  30. Graphing-Inequalities Edexcel Higher
    2 主题
  31. Solving-Inequalities Edexcel Higher
    2 主题
  32. Real-Life-Graphs Edexcel Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Edexcel Higher
    2 主题
  34. Equation-Of-A-Circle Edexcel Higher
    2 主题
  35. Graphs-Of-Functions Edexcel Higher
    6 主题
  36. Linear-Graphs Edexcel Higher
    4 主题
  37. Coordinate-Geometry Edexcel Higher
    4 主题
  38. Functions Edexcel Higher
    3 主题
  39. Forming-And-Solving-Equations Edexcel Higher
    3 主题
  40. Iteration Edexcel Higher
    1 主题
  41. Simultaneous-Equations Edexcel Higher
    2 主题
  42. Quadratic-Equations Edexcel Higher
    4 主题
  43. Linear-Equations Edexcel Higher
    1 主题
  44. Algebraic-Proof Edexcel Higher
    1 主题
  45. Rearranging-Formulas Edexcel Higher
    2 主题
  46. Algebraic-Fractions Edexcel Higher
    4 主题
  47. Completing-The-Square Edexcel Higher
    1 主题
  48. Factorising Edexcel Higher
    6 主题
  49. Expanding-Brackets Edexcel Higher
    3 主题
  50. Algebraic-Roots-And-Indices Edexcel Higher
    1 主题
  51. Introduction Edexcel Higher
    7 主题
  52. Using-A-Calculator Edexcel Higher
    1 主题
  53. Surds Edexcel Higher
    2 主题
  54. Rounding-Estimation-And-Bounds Edexcel Higher
    2 主题
  55. Fractions-Decimals-And-Percentages Edexcel Higher
    3 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Higher
    4 主题
  57. Percentages Edexcel Higher
    3 主题
  58. Fractions Edexcel Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Edexcel Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Edexcel Higher
    4 主题
  61. Number-Operations Edexcel Higher
    10 主题
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Exam code:1MA1

Circles & segments

Circle Theorem: Angles in the same segment are equal

  • Any two angles on the circumference of a circle that are formed from the same two points on the circumference are equal

    • These two angles are in the same segment of the circle

      • To see this, add the chord PQ below to split the circle into two segments

A circle with points P and Q and the arc between them highlighted. Two chords from each point meet at another point on the circumference forming an angle y.

  • To spot this circle theorem on a diagram

    • Find two points on the circumference that meet at a third point

    • See if there are any other pairs of lines from the same two original points that meet at a different point on the circumference

  • When explaining this theorem in an exam you must use the keywords:

    • Angles in the same segment are equal

  • Look out for a bowtie shape

    • The theorem works upside down, in that the angles at P and Q are also equal

Angles in the same segment are equal (this works upside-down too)

Examiner Tips and Tricks

  • An exam question diagram may have multiple equal angles

    • Look for as many as possible by seeing how many pairs of lines start from the same two points on the circumference

Worked Example

The diagram below shows a circle with centre, O.
A, B, C, D and E are five points on the circumference on the circle.

Angle AEB = 12º.
Angle BEC = 14º.
Angle CED = 73º.
Angle EBD = θº.

Find the value of θ .

A circle with centre, O, and 5 points on the circumference, A, B, C, D and E. Angle AEB = 12º, angle BEC = 14º and angle CED = 73º. The angle EBC = θ º.

CE is a diameter
This means that triangles EAC and CED are both triangles in a semicircle

Angle EAC = 90º
Angle CED = 90º
Angle in a semicircle = 90º

Find the other angles in the triangles

Angle ECA = 64º
Angle ECD = 17º
Angles in a triangle = 180º

Label these angles on the diagram

Previous circle diagram with the angle EAC and EDC marked as right angles. Angle ACE = 64º and angle DCE = 17º are also labelled.

Angle θ is formed by two lines coming from either end of the chord ED
Angle ECD is also formed by two lines coming from either end of the chord ED

Angle θ = angle ECD = 17º
Angles in the same segment are equal

Angle θ = 17º

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