积极 AI Logo 积极 AI

圆内接四边形对角互补（含切线-弦角）

圆内接四边形对角互补（含切线-弦角）
几何画板及绘图内容加载中，请稍等……
2019-12-24 22:59
圆多边形角几何作图
①本范例演示圆内接四边形的对角互补性质，并展示切线与弦形成的角；②核心概念包括圆内接四边形、对角互补、切线角、弦切角；③作图要点：使用 Circle, Point, Intersect, Tangent, CircleArc, Segment, Angle, CircleSector, Rotate 等命令构造图形；④适合高中数学教学，用于理解圆与四边形的关系及角度性质。

GeoGebra 命令及参数

  1. Circle(O, 1) → c
  2. Point(c) → C
  3. Circle(C, 0.3) → q
  4. Intersect(c, q, 2) → P
  5. Point(c) → A
  6. Intersect(c, q, 1) → N
  7. Tangent(A, c) → j,
  8. CircleArc(O, N, A) → d
  9. Point(d) → D
  10. CircleArc(O, A, P) → e
  11. Point(e) → B
  12. Segment(C, D) → f
  13. Segment(D, A) → g
  14. Segment(A, B) → h
  15. Segment(B, C) → i
  16. Circle(A, 1.5) → p
  17. Intersect(p, j, 2) → F
  18. Intersect(p, j, 1) → E
  19. If(k ≤ 1, k, 1) → k1
  20. If(k ≤ 1, 0, 1 < k ≤ 2, k - 1, 1) → k2
  21. If(k ≤ 2, 0, 2 < k ≤ 3, k - 2, 1) → k3
  22. If(k ≤ 3, 0, 3 < k ≤ 4, k - 3, 1) → k4
  23. Segment(G, H) → l
  24. Segment(C, I) → m
  25. Angle(B, A, D) → α
  26. Intersect(q, f, 1) → J
  27. Intersect(q, i, 1) → K
  28. Intersect(q, m, 1) → L
  29. CircleSector(C, J, L) → s1
  30. CircleSector(C, L, K) → s2
  31. Rotate(Translate[s1, Vector[(k3 * Vector[C, A])]], ((-k3) * Angle[A, D, C]), M) → s1'
  32. Rotate(Translate[s2, Vector[(k3 * Vector[C, A])]], (k3 * Angle[C, B, A]), M) → s2'
  33. Angle(D, C, B) → r