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Frank's Circles Problem: Change Circle Number

Frank's Circles Problem: Change Circle Number
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2015-06-06 01:48
CircleGeometric Construction
This example demonstrates a geometric challenge problem for students, showing how to break down a region into shapes to find a solution. It involves core math concepts like area, circle, perimeter, and geometric construction. Constructed using GeoGebra commands such as Point, Circle, Intersect, CircleArc, Segment, Polygon, and CircleSector. Ideal for high school mathematics education, enhancing geometric construction and problem-solving skills.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Circle(A, r) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, r) → d
  5. Intersect(d, xAxis, 2) → C
  6. Circle(C, r) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(d, e, 2) → F
  10. Intersect(c, d, 2) → G
  11. CircleArc(A, D, G) → f
  12. CircleArc(B, G, F) → g
  13. CircleArc(C, F, E) → h
  14. CircleArc(B, E, D) → k
  15. Segment(A, D) → a
  16. Polygon(D, A, G, B) → poly1, d_1, a_1, g_1, b
  17. Polygon(E, B, F, C) → poly2, e_1, b_1, f_1, c_1
  18. CircleSector(A, D, G) → p
  19. CircleSector(B, E, D) → q
  20. CircleSector(B, G, F) → r_1
  21. CircleSector(C, F, E) → s
  22. Intersect(e, xAxis, 2) → H
  23. Circle(H, r) → t
  24. Intersect(c, g_1, 1) → I
  25. Intersect(c, d, 2) → J
  26. Intersect(c, d, 1) → K
  27. CircleArc(I, J, K) → h_1
  28. CircleSector(I, J, K) → k_1
  29. Intersect(e, t, 1) → L
  30. Intersect(e, xAxis, 2) → M
  31. Intersect(e, t, 2) → N
  32. Intersect(d, t, 1) → O
  33. Polygon(L, M, N, O) → poly3, l_1, m, n_1, o
  34. Intersect(d, e, 1) → P
  35. CircleSector(O, L, P) → p_1
  36. Intersect(d, e, 2) → Q
  37. CircleSector(O, Q, N) → q_1
  38. CircleSector(M, N, L) → s_1
  39. CircleArc(O, L, P) → t_1
  40. CircleArc(O, Q, N) → c_2
  41. CircleArc(M, N, L) → d_2
  42. Intersect(t, xAxis, 2) → R
  43. Circle(R, r) → e_2
  44. Intersect(t, e_2, 1) → S
  45. Intersect(t, e_2, 2) → T
  46. Polygon(S, R, T, M) → poly4, s_2, r_2, t_2, m_1
  47. CircleSector(M, S, L) → f_2
  48. CircleSector(M, N, T) → g_2
  49. CircleSector(R, T, S) → h_2
  50. CircleArc(M, S, L) → k_2
  51. CircleArc(M, N, T) → p_2
  52. CircleArc(R, T, S) → q_2