MathPlotAI Logo MathPlotAI

Circle Tangent-Types Illustrator

Circle Tangent-Types Illustrator
Loading the math board and drawing, please wait…
2019-06-29 05:43
CircleAngleGeometric Construction
This example demonstrates the types of tangents to a circle, including external and internal tangents. It involves core mathematical concepts such as circles, tangent lines, similar triangles, angles, and distance calculations. The construction utilizes GeoGebra commands like Circle, Segment, PointIn, Distance, Tangent, Intersect, Dilate, and Angle. It is suitable for high school mathematics education, helping students visualize and understand the properties and geometric relationships of circle tangents.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. PointIn(a) → C
  4. Distance(C, c) → b
  5. Circle(C, d) → e
  6. Tangent(c, e) → g, h, i, j
  7. Intersect(c, h) → D
  8. Intersect(c, j) → E, N
  9. Intersect(e, j) → F
  10. Intersect(e, h) → G, L
  11. Intersect(e, g) → H, K
  12. Intersect(e, i) → I
  13. Intersect(c, i) → J, M
  14. Intersect(c, g) → O
  15. Circle(D, 2) → p
  16. Circle(E, 2) → q
  17. Circle(O, 2) → r
  18. Circle(K, 2) → s
  19. Circle(I, 2) → t
  20. Circle(F, 2) → c_1
  21. Circle(G, 2) → d_1
  22. Circle(J, 2) → e_1
  23. Intersect(e_1, i, 1) → P
  24. Intersect(e_1, i, 2) → Q
  25. Intersect(p, h, 1) → R
  26. Intersect(p, h, 2) → S
  27. Intersect(c_1, j, 2) → T
  28. Intersect(c_1, j, 1) → U
  29. Intersect(d_1, h, 1) → V
  30. Intersect(d_1, h, 2) → W
  31. Intersect(s, g, 2) → Z
  32. Intersect(s, g, 1) → A_1
  33. Intersect(r, g, 2) → B_1
  34. Intersect(r, g, 1) → C_1
  35. Intersect(q, j, 2) → D_1
  36. Intersect(q, j, 1) → E_1
  37. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  38. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], M) → A'_1
  39. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], E) → A'_2
  40. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], O) → A'_3
  41. Angle(A, O, C_1) → α
  42. Angle(A, E, E_1) → β
  43. Angle(A, J, Q) → γ
  44. Angle(A, D, S) → δ
  45. Angle(C, K, A_1) → ε
  46. Intersect(t, i, 1) → F_1
  47. Angle(C, I, F_1) → ζ
  48. Angle(C, F, T) → η
  49. Angle(C, G, W) → θ
  50. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], G) → C'
  51. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], F) → C'_1
  52. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], I) → C'_2
  53. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], K) → C'_3
  54. Segment(A, A') → l
  55. Segment(A, A'_1) → m
  56. Segment(A, A'_2) → n
  57. Segment(A, A'_3) → f_1
  58. Segment(C, C') → g_1
  59. Segment(C, C'_1) → h_1
  60. Segment(C, C'_2) → i_1
  61. Segment(C, C'_3) → j_1
  62. Intersect(i, j) → G_1
  63. Intersect(i, j) → H_1