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Painting Circles

Painting Circles
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2018-11-04 00:23
CircleCoordinate GeometryMatrixTransformation
This example demonstrates how to draw circles and related geometric elements using GeoGebra. It involves core mathematical concepts such as circles, coordinate geometry, geometric transformations, and matrix operations. Key GeoGebra commands/objects used include Polygon, Midpoint, Circle, Intersect, Line, Rotate, and Tangent. Suitable for high school mathematics teaching, explaining properties of circles, geometric transformations, and applications of coordinate 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_{laranja}, 1) → d
  38. Circle(C_{verde}, 1) → e
  39. Circle(C_{roxo}, 1) → p
  40. Circle(C_{c2}, 1) → c_2purple
  41. Circle(C_{c2}, 1) → c_2green
  42. Circle(C_{c2}, 1) → c_2gray
  43. Circle(C_{c1}, 1) → c_1gray
  44. Circle(C_{c1}, 1) → c_1purple
  45. Circle(C_{c1}, 1) → c_1green
  46. Circle(C_{c3}, 1) → c_3orange
  47. Circle(C_{c3}, 1) → c_3green
  48. Circle(C_{c3}, 1) → c_3purple
  49. Circle(C_{c4}, 1) → c_4orange
  50. Circle(C_{c4}, 1) → c_4green
  51. Circle(C_{c4}, 1) → c_4purple
  52. Circle(C_{c5}, 1) → c_5orange
  53. Circle(C_{c5}, 1) → c_5green
  54. Circle(C_{c5}, 1) → c_5purple
  55. Circle(C_{c6}, 1) → c_6green
  56. Circle(C_{c6}, 1) → c_6purple
  57. Circle(C_{c6}, 1) → c_6orange
  58. Circle(C_{c7}, 1) → c_7orange
  59. Circle(C_{c7}, 1) → c_7green
  60. Circle(C_{c7}, 1) → c_7purple
  61. Circle(C_{c8}, 1) → c_8green
  62. Circle(C_{c8}, 1) → c_8orange
  63. Circle(C_{c8}, 1) → c_8purple
  64. Circle(C_{c9}, 1) → c_9green
  65. Circle(C_{c9}, 1) → c_9purple
  66. Circle(C_{c9}, 1) → c_9orange
  67. Circle(C_{c10}, 1) → c_{10}green
  68. Circle(C_{c10}, 1) → c_{10}purple
  69. Circle(C_{c10}, 1) → c_{10}orange

AI Drawing Prompt Reference

Draw a figure consisting of three triangles, each vertex on a different colored circle. The centers of these circles are the centroids of the triangles. Small circles are drawn at the midpoints of each triangle, and lines connect these midpoints. Tangents are drawn from the points where the lines intersect the circles, and the intersection points of these tangents are connected to form another polygon.
The prompt above was compiled from the original drawing commands and is for reference only.