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圆的外公切线

圆的外公切线
几何画板及绘图内容加载中，请稍等……
2016-06-26 19:55
圆解析几何几何作图
①本范例演示了如何绘制圆的外公切线及其相关几何性质；②涉及的核心数学概念包括圆、切线、角、相交线、解析几何等；③作图要点提炼自构造摘要，使用了If、Circle、Point、Segment、Tangent、Intersect、Angle、rectangle2endpointsthin、rectanglefrom2endpoints、Polygon、IsInRegion、Element、rectangle2endpointsthin1等GeoGebra命令和对象；④适合高中阶段学习几何作图、圆的性质及解析几何的学生使用。

GeoGebra 命令及参数

  1. If(SelectedIndex[listAnsQ3] ≟ 4, true, false) → Qn3correct
  2. If(SelectedIndex[listAnsQ1] ≟ 5, true, false) → Qn1correct
  3. If(SelectedIndex[listAnsQ5] ≟ 5, true, false) → Qn5correct
  4. If(SelectedIndex[listAnsQ2] ≟ 3, true, false) → Qn2correct
  5. If(SelectedIndex[listAnsQ4] ≟ 5, true, false) → Qn4correct
  6. Circle(O, R) → c
  7. Point(c) → F
  8. Segment(O, F) → e
  9. Tangent(F, c) → b,
  10. Point(b) → D
  11. Point(b) → C
  12. Segment(C, D) → g
  13. Point(c) → E
  14. Tangent(E, c) → a,
  15. Point(a) → B
  16. Point(a) → A
  17. Segment(A, B) → h
  18. Intersect(g, h) → S
  19. Segment(O, S) → f
  20. Circle(O, (0.13 * Distance[O, S])) → c_1
  21. Intersect(c_1, e) → I,
  22. Intersect(c_1, f) → H,
  23. Segment(O, E) → d
  24. Intersect(c_1, d) → G,
  25. Segment(E, S) → m
  26. Circle(S, (0.25 * Distance[O, S])) → p
  27. Intersect(p, m) → L,
  28. Intersect(p, f) → J,
  29. Segment(F, S) → n
  30. Intersect(p, n) → K,
  31. Angle(O, E, B) → α
  32. Angle(O, F, D) → β
  33. rectangle2endpointsthin(E, L) → poly1
  34. rectangle2endpointsthin(F, K) → poly2
  35. rectangle2endpointsthin(O, J) → poly3
  36. rectanglefrom2endpoints(O, E) → poly4
  37. rectanglefrom2endpoints(O, F) → poly5
  38. Polygon(G, H, O) → poly6, t, a_1, b_1
  39. Polygon(H, I, O) → poly7, i, d_1, e_1
  40. Polygon(J, K, S) → poly8, j, k, q
  41. Polygon(J, L, S) → poly9, l, r, s
  42. IsInRegion(K_p, poly5) → touchOF
  43. IsInRegion(K_p, poly4) → touchOE
  44. Element(listFeedbackQ5, SelectedIndex[listAnsQ5]) → txtQ5F
  45. Element(listFeedbackQ2, SelectedIndex[listAnsQ2]) → txtQ2F
  46. Segment(O, S) → f_d
  47. Angle(S, O, E) → γ
  48. Segment(O, F) → e_d
  49. Segment(O, E) → d_d
  50. Angle(F, O, S) → δ
  51. Angle(O, S, F) → ε
  52. Angle(E, S, O) → ζ
  53. rectangle2endpointsthin1(C, D) → poly10LineCD
  54. rectangle2endpointsthin1(A, B) → poly11LineAB
  55. IsInRegion(K_p, poly10LineCD) → touchCD
  56. IsInRegion(K_p, poly11LineAB) → touchAB