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Symmetry of Peripheral Circles

Symmetry of Peripheral Circles
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2019-08-13 00:39
CirclePolygonTransformation
This example demonstrates the symmetry of peripheral circles of polygons. Key math concepts include circle, polygon, symmetry, and geometric transformations. It is constructed using GeoGebra commands like Circle, Point, Line, Intersect, Polygon, and Segment, making it suitable for high school students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Circle(A, a / 2) → q
  2. Point(q) → K
  3. Line(K, A) → s
  4. Intersect(q, s, 2) → I
  5. Point(Circle[A, a]) → B
  6. Circle(B, a / 2) → p
  7. Intersect(p, q) → T, , ,
  8. Point(p) → L
  9. Line(L, B) → k_1
  10. Intersect(p, k_1, 2) → R
  11. Polygon(A, B, 6) → poly1, g, F, h_2, i, j, k, l, C, D, E
  12. Circle(F, a / 2) → r
  13. Intersect(r, q) → V, , ,
  14. Point(r) → J
  15. Line(J, F) → g_1
  16. Intersect(r, g_1, 2) → O
  17. Circle(C, a / 2) → e
  18. Point(e) → M
  19. Line(M, C) → i_1
  20. Intersect(e, i_1, 2) → Q
  21. Circle(D, a / 2) → d
  22. Intersect(e, d) → U, , ,
  23. Segment(U, V) → n_1
  24. Point(d) → N
  25. Line(N, D) → b
  26. Intersect(d, b, 2) → P
  27. Circle(E, a / 2) → c
  28. Intersect(d, c) → S, , ,
  29. Segment(S, T) → m_1
  30. Intersect(m_1, n_1) → W
  31. Segment(P, W) → g_2
  32. Segment(N, W) → f_2
  33. Segment(M, W) → e_1
  34. Segment(Q, W) → d_1
  35. Segment(R, W) → c_1
  36. Segment(L, W) → b_1
  37. Segment(I, W) → a_1
  38. Segment(K, W) → t_1
  39. Segment(O, W) → s_1
  40. Segment(J, W) → r_1
  41. Point(c) → H
  42. Segment(H, W) → q_1
  43. Line(H, E) → f
  44. Intersect(c, f, 2) → G
  45. Segment(G, W) → p_1
  46. Line(J, E) → f_1
  47. Segment(H, G) → m
  48. Segment(J, O) → n
  49. Segment(I, K) → t
  50. Segment(P, N) → h_1
  51. Segment(Q, M) → j_1
  52. Segment(L, R) → l_1