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Circles at Polygon Vertices

Circles at Polygon Vertices
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2015-05-27 12:30
CirclePolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates circles centered at the vertices of polygons. Key mathematical concepts include circles, polygons, and vectors. Using GeoGebra commands such as Polygon, Point, Circle, Segment, and Intersect, one can construct polygons and circles at their vertices. Suitable for middle school and above students to learn geometric construction and properties of circles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Polygon(A', B', C', D', E') → poly2, e, f, g, h, i
  3. Polygon(A'', B'', C'', D'', E'', F'') → poly3, j, k, l, m, n, o
  4. Point(a) → E
  5. Circle(A, E) → c_1
  6. Segment(E, A) → a_1
  7. Circle(B, E) → d_1
  8. Intersect(d_1, b, 1) → F
  9. Segment(E, B) → b_1
  10. Segment(B, F) → e_1
  11. Circle(C, F) → f_1
  12. Intersect(f_1, c, 1) → G
  13. Segment(C, F) → g_1
  14. Segment(C, G) → h_1
  15. Circle(D, G) → k_1
  16. Intersect(k_1, d, 1) → H
  17. Segment(G, D) → i_1
  18. Segment(D, H) → j_1
  19. Intersect(c_1, d, 1) → H_1
  20. Segment(A, H_1) → l_1
  21. Point(e) → F'
  22. Circle(A', F') → p_1
  23. Circle(B', F') → q_1
  24. Intersect(q_1, f, 1) → G'
  25. Circle(C', G') → r_1
  26. Intersect(r_1, g, 1) → H'
  27. Circle(D', H') → s_1
  28. Intersect(s_1, h, 1) → I'
  29. Circle(E', I') → t_1
  30. Intersect(t_1, i, 1) → J'
  31. Intersect(p_1, i, 1) → J'_1
  32. Segment(A', F') → m_1
  33. Segment(A', J'_1) → n_1
  34. Segment(F', B') → a_2
  35. Segment(B', G') → b_2
  36. Segment(G', C') → c_2
  37. Segment(H', C') → d_2
  38. Segment(D', H') → e_2
  39. Segment(D', I') → f_2
  40. Segment(E', I') → g_2
  41. Segment(E', J') → h_2
  42. Circle(Intersect[AngularBisector[C, B, A], AngularBisector[D, C, B]], Intersect[OrthogonalLine[Intersect[AngularBisector[C, B, A], AngularBisector[D, C, B]], a], a]) → k_2
  43. Point(j) → G''
  44. Circle(A'', G'') → p_2
  45. Circle(B'', G'') → q_2
  46. Intersect(q_2, k, 1) → H''
  47. Circle(C'', H'') → r_2
  48. Intersect(r_2, l, 1) → I''
  49. Circle(D'', I'') → s_2
  50. Intersect(s_2, m, 1) → J''
  51. Circle(E'', J'') → t_2
  52. Intersect(t_2, n, 1) → K''
  53. Circle(F'', K'') → c_3
  54. Intersect(c_3, o, 1) → L''
  55. Intersect(p_2, o, 1) → L''_1
  56. Segment(A'', G'') → i_2
  57. Segment(A'', L''_1) → j_2
  58. Segment(G'', B'') → l_2
  59. Segment(B'', H'') → m_2
  60. Segment(C'', H'') → n_2
  61. Segment(C'', I'') → a_3
  62. Segment(I'', D'') → b_3
  63. Segment(J'', D'') → d_3
  64. Segment(J'', E'') → e_3
  65. Segment(K'', E'') → f_3
  66. Segment(K'', F'') → g_3
  67. Segment(L'', F'') → h_3