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Circle Sectors and Related Rectangle Area

Circle Sectors and Related Rectangle Area
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2020-05-15 03:14
CircleTrigonometryGeometric Construction
This example demonstrates the relationship between the area of a circle sector and its related rectangle. It involves core mathematical concepts such as circle area, sector area, rectangle area, and trigonometry. The construction uses GeoGebra commands like Intersect, Circle, Rotate, Angle, CircleSector, Segment, Midpoint, and Mirror. Suitable for high school mathematics education to understand area calculations and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 4) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, 18°, A) → B'
  5. Angle(B, A, B') → α
  6. CircleSector(A, B, B') → d
  7. Segment(A, B') → f
  8. Midpoint(f) → C
  9. Mirror(d, C) → d'
  10. Point(d') → D
  11. Segment(D, B') → g
  12. Midpoint(g) → E
  13. Mirror(d', E) → d''
  14. Point(d'') → F
  15. Segment(D, F) → h
  16. Midpoint(h) → G
  17. Mirror(d'', G) → d'''
  18. Point(d''') → H
  19. Segment(H, F) → i
  20. Midpoint(i) → I
  21. Mirror(d''', I) → e
  22. Point(e) → J
  23. Segment(H, J) → j
  24. Midpoint(j) → K
  25. Mirror(e, K) → e'
  26. Point(e') → L
  27. Segment(L, J) → k
  28. Midpoint(k) → M
  29. Mirror(e', M) → e''
  30. Point(e'') → N
  31. Segment(L, N) → l
  32. Midpoint(l) → O
  33. Mirror(e'', O) → e'''
  34. Point(e''') → P
  35. Segment(P, N) → m
  36. Midpoint(m) → Q
  37. Mirror(e''', Q) → p
  38. Point(p) → R
  39. Segment(P, R) → n
  40. Midpoint(n) → S
  41. Mirror(p, S) → p'
  42. Point(p') → T
  43. Segment(T, R) → q
  44. Midpoint(q) → U
  45. Mirror(p', U) → p''
  46. Point(p'') → V
  47. Segment(T, V) → r
  48. Midpoint(r) → W
  49. Mirror(p'', W) → p'''
  50. Point(p''') → Z
  51. Segment(Z, V) → s
  52. Midpoint(s) → A_1
  53. Mirror(p''', A_1) → t
  54. Point(t) → B_1
  55. Segment(Z, B_1) → a
  56. Midpoint(a) → C_1
  57. Mirror(t, C_1) → t'
  58. Point(t') → D_1
  59. Segment(D_1, B_1) → b
  60. Midpoint(b) → E_1
  61. Mirror(t', E_1) → t''
  62. Point(t'') → F_1
  63. Segment(D_1, F_1) → f_1
  64. Midpoint(f_1) → G_1
  65. Mirror(t'', G_1) → t'''
  66. Segment(A, B) → g_1
  67. Midpoint(g_1) → H_1
  68. Mirror(d, H_1) → d'_1
  69. Point(d'_1) → I_1
  70. Segment(I_1, B) → h_1
  71. Midpoint(h_1) → J_1
  72. Mirror(d'_1, J_1) → c_1
  73. Point(c_1) → K_1
  74. Segment(I_1, K_1) → i_1
  75. Midpoint(i_1) → L_1
  76. Mirror(c_1, L_1) → d_1
  77. Point(d_1) → M_1
  78. Segment(M_1, K_1) → j_1
  79. Midpoint(j_1) → N_1
  80. Mirror(d_1, N_1) → e_1
  81. Intersect(c, xAxis, 1) → O_1
  82. Rotate(O_1, 10°, A) → P_1
  83. Angle(O_1, A, P_1) → β
  84. CircleSector(A, O_1, P_1) → k_1