WEILAI Online Academic assistant
WEILAI Online Academic assistant
Back to 课程

Maths Gcse Aqa Higher

0% Complete
0/0 Steps
  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
    3 主题
  9. Transformations Aqa Higher
    5 主题
  10. Vectors Aqa Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
    4 主题
  13. Pythagoras-And-Trigonometry Aqa Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
    1 主题
  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
    2 主题
  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
    3 主题
  22. Symmetry-And-Shapes Aqa Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Aqa Higher
    2 主题
  24. Standard-And-Compound-Units Aqa Higher
    5 主题
  25. Direct-And-Inverse-Proportion Aqa Higher
    2 主题
  26. Problem-Solving-With-Ratios Aqa Higher
    2 主题
  27. Ratios Aqa Higher
    3 主题
  28. Sequences Aqa Higher
    4 主题
  29. Transformations-Of-Graphs Aqa Higher
    2 主题
  30. Graphing-Inequalities Aqa Higher
    2 主题
  31. Solving-Inequalities Aqa Higher
    2 主题
  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
    2 主题
  35. Functions Aqa Higher
    3 主题
  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
    4 主题
  40. Iteration Aqa Higher
    1 主题
  41. Simultaneous-Equations Aqa Higher
    2 主题
  42. Quadratic-Equations Aqa Higher
    4 主题
  43. Linear-Equations Aqa Higher
    1 主题
  44. Algebraic-Proof Aqa Higher
    1 主题
  45. Rearranging-Formulas Aqa Higher
    2 主题
  46. Algebraic-Fractions Aqa Higher
    4 主题
  47. Completing-The-Square Aqa Higher
    1 主题
  48. Factorising Aqa Higher
    6 主题
  49. Expanding-Brackets Aqa Higher
    3 主题
  50. Algebraic-Roots-And-Indices Aqa Higher
    1 主题
  51. Using-A-Calculator Aqa Higher
    1 主题
  52. Surds Aqa Higher
    2 主题
  53. Rounding-Estimation-And-Bounds Aqa Higher
    2 主题
  54. Fractions-Decimals-And-Percentages Aqa Higher
    3 主题
  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
    4 主题
  61. Number-Operations Aqa Higher
    10 主题
课 Progress
0% Complete

Exam code:8300

Cyclic quadrilaterals

Circle theorem: Opposite angles in a cyclic quadrilateral add up to 180°

  • A quadrilateral that is formed by four points on the circumference of a circle, (a cyclic quadrilateral), will have pairs of opposite angles that add up to 180°

A circle with points A, B, C and D on its circumference. The quadrilateral ABCD formed is a cyclic quadrilateral.

  • To spot this theorem in a diagram

    • look for quadrilaterals that have all four points on the circumference

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

    • Opposite angles in a cyclic quadrilateral add up to 180°

  • The theorem only works for cyclic quadrilaterals

    • The diagram below shows a common scenario that is not a cyclic quadrilateral

Not cyclic quad point at centre, IGCSE & GCSE Maths revision notes

Examiner Tips and Tricks

  • Cyclic quadrilaterals are often easy to spot in a busy diagram

    • Mark on their angles (even if you think you don’t need them) as they may help you later on!

Worked Example

The circle below has centre, O.

Find the value of x.

Q1 Circle Theorems 3, IGCSE & GCSE Maths revision notes

Identify both the cyclic quadrilateral and the radius perpendicular to the chord

Add to the diagram as you work through the problem

Q1 CT3 Working in red, IGCSE & GCSE Maths revision notes

The radius bisects the chord and so creates two congruent triangles

Use this to work out 72° (equal to the equivalent angle in the other triangle)
And 18° (angles in a triangle add up to 180°)

Then use that opposite angles in a cyclic quadrilateral add up to 180°

table row cell 2 x plus 4 plus 20 plus 18 end cell equals 180 row cell 2 x end cell equals 138 end table

<img alt=”bold italic x bold equals bold 69 bold degree” data-mathml=”<math ><semantics><mrow><mi mathvariant=”bold-italic”>x</mi><mo mathvariant=”bold”>=</mo><mn mathvariant=”bold”>69</mn><mo mathvariant=”bold”>&#176;</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></semantics></math>” data-type=”finalAnswer” height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2259%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathvariant%3D%22bold-italic%22%3Ex%3C%2Fmi%3E%3Cmo%20mathvariant%3D%22bold%22%3E%3D%3C%2Fmo%3E%3Cmn%20mathvariant%3D%22bold%22%3E69%3C%2Fmn%3E%3Cmo%20mathvariant%3D%22bold%22%3E%26%23xB0%3B%3C%2Fmo%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math123919e9c7f188e0f3ae690e7e2’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABTGhlYWQQC2qxAAAC4AAAADZoaGVhCGsXSAAAAxgAAAAkaG10eE2rRkcAAAM8AAAADGxvY2EAHTwYAAADSAAAABBtYXhwBT0FPgAAA1gAAAAgbmFtZaBxlY4AAAN4AAABn3Bvc3QB9wD6AAAFGAAAACBwcmVwa1uragAABTgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACAD0AsP%2F%2FAAAAPQCw%2F%2F%2F%2FxP9SAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgADrAtUCFQADAAcAZRgBsAgQsAbUsAYQsAXUsAgQsAHUsAEQsADUsAYQsAc8sAUQsAQ8sAEQsAI8sAAQsAM8ALAIELAG1LAGELAH1LAHELAB1LABELAC1LAGELAFPLAHELAEPLABELAAPLACELADPDEwEyE1IR0BITWAAlX9qwJVAcBV1VVVAAIAVQHWAasDKwALABcASRgBsBgQsQgF9LESBfSxDwX0sQwF9LECBfSxGQX0swsVBQ8QPDw8ALAYELELAvSxDwX0sRIF9LEVBfSxBQX0swgMAhIQPDw8MDEAFhUUBiMuATc0Nh8BNCYjJgYVFBYXMjYBVlVVVlVWAVVVVSorKisrKisqAypVVVVVAVRWVVUBqisqASorKyoBKgABAAAAAQAA1XjOQV8PPPUAAwQA%2F%2F%2F%2F%2F9Y6E3P%2F%2F%2F%2F%2F1joTcwAA%2FyAEgAOrAAAACgACAAEAAAAAAAEAAAPo%2F2oAABdwAAD%2FtgSAAAEAAAAAAAAAAAAAAAAAAAADA1IAVQNWAIACAABVAAAAAAAAACgAAACyAAABTAABAAAAAwBeA

Responses

您的邮箱地址不会被公开。 必填项已用 * 标注