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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
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  5. Averages-Ranges-And-Data Aqa Higher
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  6. Combined-And-Conditional-Probability Aqa Higher
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  7. Tree-Diagrams Aqa Higher
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  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  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
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  16. Volume-And-Surface-Area Aqa Higher
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  17. Circles-Arcs-And-Sectors Aqa Higher
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  18. Area-And-Perimeter Aqa Higher
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  19. Circle-Theorems Aqa Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
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  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
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  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
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  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
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  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
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  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
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  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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  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
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  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
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  57. Percentages Aqa Higher
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  58. Fractions Aqa Higher
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  59. Powers-Roots-And-Standard-Form Aqa Higher
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  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
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  61. Number-Operations Aqa Higher
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Exam code:8300

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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