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Circle - Central Angle and Intercepted Arc

Circle - Central Angle and Intercepted Arc
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2015-04-09 04:36
CircleAngleGeometric Construction
This example demonstrates the relationship between the central angle and the intercepted arc in a circle. Key mathematical concepts include circle, angle, and arc. Using GeoGebra commands such as Circle, Angle, and ArcDeg, the example dynamically shows how the intercepted arc changes with the central angle. Suitable for middle school and above students to learn about circle properties.

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) → inputBox4
  32. Textfield(YourCircumference) → inputBox5
  33. Textfield(YourSectorAOC) → inputBox6
  34. Textfield(YourArcACLength) → inputBox7
  35. Textfield(YourAngleAOC) → inputBox8
  36. Textfield(YourAngleFOD) → inputBox9
  37. Textfield(YourArcACdegree) → inputBox10
  38. Textfield(YourArcFDdegree) → inputBox11
  39. Textfield(YourRadius) → inputBox12
  40. Textfield(YourDiameter) → inputBox13
  41. CircumcircleSector(A, B, C) → f

AI Drawing Prompt Reference

Draw a circle with center O and radius r. Select two points A and C on the circle such that ∠AOC is α degrees and the arc length AC is d degrees. Then select point D on the circle such that ∠COD is β degrees and the arc length FD is e degrees. Finally, draw the circumference and area of the circle, and label the central angle ∠AOC, the inscribed angle ∠BAC, the inscribed angle ∠FOD, the degree of arc AC, and the degree of arc FD.
The prompt above was compiled from the original drawing commands and is for reference only.