Circle Tangent-Types Illustrator by Tim Brzezinski

Circle Tangent-Types Illustrator by Tim Brzezinski
Loading the math board and drawing, please wait…
2016-12-16 00:01
In collections Circles (Theorems)
This example demonstrates how to construct circles and their tangent lines using geometric principles. Key mathematical concepts include circle properties, tangent line definitions, distance calculations, and geometric transformations. The construction involves using GeoGebra commands such as Circle, Tangent, Intersect, and Dilate with various objects like A, B, C, etc. It is suitable for high school students or math enthusiasts to understand the relationship between circles and tangents, and to practice geometric construction skills.

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

AI Drawing Prompt Reference

Draw a circle and its tangent lines to illustrate geometric construction. Start by drawing a circle and a line segment, then place a point on the segment and draw another circle centered at this point. Find the intersection points of the two circles and draw tangent lines from these points. Next, draw small circles at the tangent points and find their intersections with the larger circles. Finally, create new points by scaling existing ones and measure angles to show geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.