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Dynamic Circle Problem Demonstration

Dynamic Circle Problem Demonstration
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2018-06-20 17:50
CircleGeometric Construction
This example dynamically illustrates a circle-related geometric problem, involving core concepts like circles, intersections, similar triangles, and transformations. It is constructed using commands such as Circle, PointIn, Intersect, Line, CircleArc, Point, Dilate, Segment, Angle, Vector, Translate, and Polygon, making it suitable for high school mathematics instruction and geometric construction learning.

GeoGebra Commands & Parameters

  1. Circle(O, B_1) → c
  2. PointIn(a) → E
  3. Semicircle(O, E) → d
  4. Intersect(c, d, 1) → A
  5. Line(E, A) → f
  6. Semicircle(E, O) → e
  7. Intersect(c, e, 1) → E_1
  8. CircleArc(O, A, E_1) → g
  9. Point(g) → D
  10. Line(E, D) → h
  11. Line(A, O) → i
  12. Intersect(c, i, 2) → B
  13. Line(E, O) → j
  14. Intersect(c, h, 1) → C
  15. Line(B, C) → k
  16. Intersect(j, k) → F
  17. Line(B, D) → l
  18. Intersect(j, l) → G
  19. Dilate(O, If[0 < b ≤ 1, 1 - b, 0], A) → O'
  20. Dilate(E, If[0 < b ≤ 1, 1 - b, 0], A) → E'
  21. Segment(O, O') → m
  22. Segment(E, E') → n
  23. Angle(O, A, E) → α
  24. Dilate(O, If[0 < b ≤ 1, 1 - b, 0], B) → O'_1
  25. Segment(O, O'_1) → p
  26. Dilate(E, If[2 < b ≤ 3, 3 - b, 0], C) → E'_1
  27. Segment(E, E'_1) → q
  28. Dilate(C, If[3 < b ≤ 4, 4 - b, 0], D) → C'
  29. Segment(C, C') → r
  30. Dilate(E, If[4 < b ≤ 5, 5 - b, 0], F) → E'_2
  31. Segment(E, E'_2) → s
  32. Intersect(c, j) → H, I
  33. Dilate(F, If[5 < b ≤ 6, 6 - b, 0], I) → F'
  34. Segment(F, F') → t
  35. Dilate(B, If[7 < b ≤ 8, 8 - b, 0], G) → B'
  36. Segment(B, B') → f_1
  37. Dilate(G, If[8 < b ≤ 9, 9 - b, 0], D) → G'
  38. Segment(G, G') → g_1
  39. Dilate(B, If[9 < b ≤ 10, 10 - b, 0], F) → B'_1
  40. Segment(B, B'_1) → h_1
  41. Dilate(F, If[10 < b ≤ 11, 11 - b, 0], C) → F'_1
  42. Segment(F, F'_1) → i_1
  43. Dilate(G, If[11 < b ≤ 12, 12 - b, 0], A) → G'_1
  44. Vector(G, G'_1) → u
  45. Translate(B, u) → B'_2
  46. Translate(B', u) → B''
  47. Segment(B'_2, B'') → j_1
  48. Dilate(F, If[12 < b ≤ 13, 13 - b, 0], A) → F'_2
  49. Vector(F, F'_2) → v
  50. Translate(B, v) → B'_3
  51. Translate(B'_1, v) → J
  52. Segment(B'_3, J) → k_1
  53. Polygon(G, B, F, A) → q1, g_2, b_1, f_2, a_1