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Eight Circles Intersection

Eight Circles Intersection
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2016-12-31 02:33
CircleCoordinate GeometryGeometric Construction
This example demonstrates the geometric formation and spatial relationships of eight intersecting circles. It involves core math concepts like circles, intersection points, angles, and geometric construction. Construction highlights include using commands such as Segment, Circle, Line, and AngularBisector to create and adjust circles. Suitable for high school and above students learning geometric construction, spatial geometry, and analytical geometry.

GeoGebra Commands & Parameters

  1. Segment(A, I) → f
  2. Segment(J, H_1) → g
  3. Segment(K, G_1) → h
  4. Segment(L, F_1) → i
  5. Segment(M, E_1) → j
  6. Segment(N, D_1) → k
  7. Segment(O, C_1) → l
  8. Segment(P, B_1) → m
  9. Segment(Q, A_1) → n
  10. Segment(A, Q) → p
  11. Segment(B, R) → q
  12. Segment(C, S) → r
  13. Segment(D, T) → s
  14. Segment(E, U) → t
  15. Segment(F, V) → a
  16. Segment(G, W) → b
  17. Segment(H, Z) → c
  18. Segment(I, A_1) → d
  19. Circle(PSeven, disksize) → e
  20. Circle(PThree, disksize) → c_2
  21. Circle(PFour, disksize) → d_1
  22. Circle(POne, disksize) → e_1
  23. Circle(PSix, disksize) → f_1
  24. Circle(PTwo, disksize) → g_1
  25. Circle(PFive, disksize) → h_1
  26. Circle(PEight, disksize) → k_1
  27. Line(POne, yAxis) → i_1
  28. Line(PTwo, i_1) → j_1
  29. Line(PThree, j_1) → l_1
  30. Line(PFour, l_1) → m_1
  31. Line(PFive, m_1) → n_1
  32. Line(PSix, n_1) → p_1
  33. Line(PSeven, p_1) → q_1
  34. Line(PEight, q_1) → r_1
  35. Line(POne, xAxis) → s_1
  36. Line(PTwo, s_1) → t_1
  37. Line(PThree, t_1) → a_1
  38. Line(PFour, a_1) → b_1
  39. Line(PFive, b_1) → c_1
  40. Line(PSix, c_1) → f_2
  41. Line(PSeven, f_2) → g_2
  42. Line(PEight, g_2) → h_2
  43. AngularBisector(s_1, i_1) → i_2, j_2
  44. AngularBisector(t_1, j_1) → k_2, l_2
  45. AngularBisector(a_1, l_1) → m_2, n_2
  46. AngularBisector(b_1, m_1) → p_2, q_2
  47. AngularBisector(c_1, n_1) → r_2, s_2
  48. AngularBisector(f_2, p_1) → t_2, a_2
  49. AngularBisector(g_2, q_1) → b_2, d_2
  50. AngularBisector(h_2, r_1) → e_2, f_3