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Area of Concentric Circles

Area of Concentric Circles
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2017-12-22 21:54
CircleCoordinate GeometryGeometric ConstructionSlider AnimationLocus
In collections Mathematics Form 2
This example demonstrates the calculation and visualization of the area of concentric circles. It involves core mathematical concepts such as the area formula of a circle, geometric construction, and coordinate geometry. The construction utilizes GeoGebra commands like VerticalLine, Point, Distance, Circle, Sequence, Zip, Segment, Midpoint, HorizontalLine, Angle, Element, SelectedIndex, If, Corner. It is suitable for high school mathematics education, helping students understand the properties of concentric circles and methods for calculating their areas.

GeoGebra Commands & Parameters

  1. VerticalLine(A) → f
  2. Point(f) → B
  3. Distance(A, B) → AB
  4. Circle(A, B) → c
  5. Sequence(Circle[A, (p * Jejari)], p, 1, b) → ListBulatan
  6. Sequence((p * Jejari / (1 - a)), p, 1, b) → ListJejari
  7. Zip(Intersect[p, f, 1], p, ListBulatan) → ListBawah
  8. Zip(Intersect[Circle[p, q], f, 2], p, ListBawah, q, ListJejari) → ListPusat
  9. Zip(Rotate[p, (-(((180 * (1 - a)))°)), q], p, ListBawah, q, ListPusat) → ListTKiri
  10. Zip(Rotate[p, ((180 * (1 - a)))°, q], p, ListBawah, q, ListPusat) → ListTKanan
  11. Zip(CircleArc[p, q, r], p, ListPusat, q, ListTKiri, r, ListBawah) → ListLKiri
  12. Zip(CircleArc[p, q, r], p, ListPusat, q, ListBawah, r, ListTKanan) → ListLKanan
  13. Segment(A, B) → j
  14. Midpoint(A, B) → C
  15. HorizontalLine(B) → g
  16. Point(g) → D
  17. Angle(A, B, D) → α
  18. Element(ListTKiri, b) → M
  19. Element(ListTKanan, b) → N
  20. Zip(Rotate[p, ((-360 * a))°, q], p, ListBawah, q, ListPusat) → ListTPutar
  21. Zip(CircleArc[p, q, r], p, ListPusat, q, ListBawah, r, ListTPutar) → ListLengkuk
  22. Element(ListTPutar, b) → P
  23. SelectedIndex(Bahasa) → nn
  24. If(nn ≟ 1, "r", "j") → text1
  25. Corner(1) → Cn
  26. Corner(2) → Cm
  27. If(h ≟ true, (abs(x(Cm) - x(Cn)) - 0.5) / ((2 * π)), i ≟ true, (abs(x(Cm) - x(A)) - 0.5) / ((2 * π))) → MaxR