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Find Central Angle Given Arc Length

Find Central Angle Given Arc Length
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2015-04-09 04:41
CircleAngleGeometric Construction
This example demonstrates how to calculate the central angle given the arc length. Key mathematical concepts include circle properties and angle measurement. Using GeoGebra commands such as `Angle`, `ArcDeg`, and `Rotate`, the relationship between the central angle and arc length is dynamically illustrated. Suitable for middle school and above students to learn geometric construction and angle calculation.

GeoGebra Commands & Parameters

  1. Element(Dimension[Arc1Arc2Radius], 1) → NumberOfEquations
  2. Random(1, NumberOfEquations) → CircleCounter
  3. Element(Arc1Arc2Radius, CircleCounter) → targetCircleCoef
  4. Textfield(h) → inputBox1
  5. Textfield(k) → inputBox2
  6. Textfield(r) → inputBox3
  7. Random(1, 4) → WhichPoint
  8. Element(targetCircleCoef, 1) → Arc1
  9. Element(targetCircleCoef, 2) → Arc2
  10. Element(targetCircleCoef, 3) → radius
  11. Circle(YourCenter, radius) → c
  12. Mod(CircleCounter + 1, NumberOfEquations + 1) → counter
  13. Point(c) → A
  14. Random(1, (360 - Arc1 - Arc2) / 2) → MissingArcBetween1and2
  15. Rotate(A, α°, YourCenter) → C
  16. Angle(A, YourCenter, C) → AngleArc1
  17. ArcDeg(c, A, C) → d, text1
  18. Rotate(C, MissingArcBetween1and2°, YourCenter) → D
  19. Angle(C, YourCenter, D) → AngleArcCD
  20. Rotate(D, Arc2°, YourCenter) → F
  21. Angle(D, YourCenter, F) → AngleArc2
  22. ArcDeg(c, D, F) → e, text3
  23. Segment(YourCenter, A) → a
  24. Segment(YourCenter, C) → b
  25. Rotate(A, (Arc1 / 2)°, YourCenter) → B
  26. Angle(A, YourCenter, B) → ε
  27. Rotate(D, (Arc2 / 2)°, YourCenter) → E
  28. Angle(D, YourCenter, E) → ζ
  29. Circumference(c) → CircCircumf
  30. Area(c) → CircArea
  31. Textfield(YourArea) → YouArea
  32. Textfield(YourCircumference) → YouCircumference
  33. Textfield(YourSectorAOC) → YouSectorAOC
  34. Textfield(YourArcACLength) → YouArcAClength
  35. Textfield(YourAngleAOC) → YouAngleAOC
  36. Textfield(YourAngleFOD) → YouAngleFOD
  37. Textfield(YourArcACdegree) → YourArcAC
  38. Textfield(YourArcFDdegree) → YourArcFD
  39. Textfield(YourRadius) → YouRadius
  40. Textfield(YourDiameter) → YouDiameter
  41. CircumcircleSector(A, B, C) → f
  42. Random((360 - Arc1) / 3, 360 - Arc1) → AngleForInscribedVertex
  43. Rotate(C, AngleForInscribedVertex°, YourCenter) → G
  44. Angle(C, YourCenter, G) → G_1
  45. Point(b) → H
  46. Segment(H, G) → g
  47. Point(d) → I
  48. Segment(G, I) → i
  49. Angle(I, G, H) → β