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Circles in Triangle - Combinatorial Geometry

Circles in Triangle - Combinatorial Geometry
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2020-06-16 12:48
TriangleCircleGeometric Construction
This example demonstrates combinatorial geometry problems involving circles in a triangle. Key mathematical concepts include combinatorial geometry, properties of circles, and triangle properties. Using GeoGebra commands such as Polygon, Circle, Intersect, etc., multiple circles and their relationships with the triangle are constructed. Suitable for high school mathematics education, particularly in geometry and combinatorial geometry.

GeoGebra Commands & Parameters

  1. Polygon(C_{c7}, C_{c10}, 3) → poly1, f, g, h, C_{c1}
  2. Midpoint(h) → D
  3. Midpoint(g) → E
  4. Midpoint(f) → F
  5. Circle(C_{c7}, 1) → c_7gray
  6. Circle(C_{c1}, 1) → c_1orange
  7. Circle(C_{c10}, 1) → c_{10}gray
  8. Intersect(c_1orange, h, 1) → G
  9. Intersect(c_1orange, g, 1) → H
  10. Intersect(c_{10}gray, g, 1) → I
  11. Intersect(c_7gray, f, 1) → J
  12. Intersect(c_7gray, h, 1) → K
  13. Intersect(c_{10}gray, f, 1) → L
  14. Midpoint(J, F) → C_{c8}
  15. Circle(C_{c8}, 1) → c_8gray
  16. Midpoint(F, L) → C_{c9}
  17. Midpoint(I, E) → C_{c6}
  18. Midpoint(E, H) → C_{c3}
  19. Midpoint(G, D) → C_{c2}
  20. Midpoint(D, K) → C_{c4}
  21. Circle(C_{c2}, 1) → c_2orange
  22. Circle(C_{c4}, 1) → c_4gray
  23. Circle(C_{c3}, 1) → c_3gray
  24. Circle(C_{c6}, 1) → c_6gray
  25. Circle(C_{c9}, 1) → c_9gray
  26. Midpoint(C_{c4}, C_{c6}) → C_{c5}
  27. Circle(C_{c5}, 1) → c_5gray
  28. Line(A, B) → i
  29. Rotate(B, 120°, C_{c10}) → B'
  30. Rotate(A, (-(120°)), C_{c7}) → A'
  31. Tangent(A', c_7gray) → j,
  32. Tangent(B', c_{10}gray) → k,
  33. Intersect(j, k) → C
  34. Intersect(i, j) → M
  35. Intersect(i, k) → N
  36. Polygon(M, N, C) → t1, c_{11}, m, n
  37. Circle(C_{c2}, 1) → c_2purple
  38. Circle(C_{c2}, 1) → c_2green
  39. Circle(C_{c2}, 1) → c_2gray
  40. Circle(C_{c1}, 1) → c_1gray
  41. Circle(C_{c1}, 1) → c_1purple
  42. Circle(C_{c1}, 1) → c_1green
  43. Circle(C_{c3}, 1) → c_3orange
  44. Circle(C_{c3}, 1) → c_3green
  45. Circle(C_{c3}, 1) → c_3purple
  46. Circle(C_{c4}, 1) → c_4orange
  47. Circle(C_{c4}, 1) → c_4green
  48. Circle(C_{c4}, 1) → c_4purple
  49. Circle(C_{c5}, 1) → c_5orange
  50. Circle(C_{c5}, 1) → c_5green
  51. Circle(C_{c5}, 1) → c_5purple
  52. Circle(C_{c6}, 1) → c_6green
  53. Circle(C_{c6}, 1) → c_6purple
  54. Circle(C_{c6}, 1) → c_6orange
  55. Circle(C_{c7}, 1) → c_7orange
  56. Circle(C_{c7}, 1) → c_7green
  57. Circle(C_{c7}, 1) → c_7purple
  58. Circle(C_{c8}, 1) → c_8green
  59. Circle(C_{c8}, 1) → c_8orange
  60. Circle(C_{c8}, 1) → c_8purple
  61. Circle(C_{c9}, 1) → c_9green
  62. Circle(C_{c9}, 1) → c_9purple
  63. Circle(C_{c9}, 1) → c_9orange
  64. Circle(C_{c10}, 1) → c_{10}green
  65. Circle(C_{c10}, 1) → c_{10}purple
  66. Circle(C_{c10}, 1) → c_{10}orange