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Angle Formed by Chord and Tangent

Angle Formed by Chord and Tangent
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2016-04-26 05:04
CircleAngleGeometric Construction
In collections Circles (Theorems)
This example demonstrates the angle formed by a chord and a tangent. Key mathematical concepts include the properties of circles and angles. Using GeoGebra commands such as Circle, Segment, OrthogonalLine, etc., the construction of the angle formed by a chord and a tangent is illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(A, C) → a
  4. OrthogonalLine(C, a) → b
  5. Rotate(C, °, A) → C'
  6. CircleArc(A, C', C) → d
  7. Point(d) → D
  8. Segment(D, C) → e
  9. Circle(A, (0.2 * a)) → f
  10. Circle(C, (0.2 * a)) → g
  11. Intersect(g, b, 2) → E
  12. Intersect(g, e, 1) → F
  13. Segment(A, C) → h
  14. Segment(A, D) → i
  15. CircleSector(C, E, F) → k
  16. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  17. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], D) → A'_1
  18. Segment(A, A'_1) → l
  19. Segment(A, A') → m
  20. Dilate(C, If[1 < j ≤ 2, 2 - j, 0], A) → C'_1
  21. Vector(C, C'_1) → u
  22. Translate(k, u) → k'
  23. Line(A, e) → n
  24. Intersect(f, i, 1) → G
  25. Intersect(f, n, 1) → H
  26. Angle(G, A, H) → α
  27. Rotate(k', If[2 < j ≤ 3, ((-(j - 2)) * α), (-α)], A) → k''
  28. Translate(E, u) → E'
  29. Rotate(E', (-α), A) → E''
  30. Intersect(f, m, 1) → I
  31. Dilate(C, If[3 < j ≤ 4, 4 - j, 0], A) → C'_2
  32. Vector(C, C'_2) → v
  33. Translate(k, v) → k'_1
  34. Angle(H, A, E'') → β
  35. Rotate(k'_1, If[4 < j ≤ 5, ((j - 4) * β), β], A) → p
  36. CircleArc(A, C, D) → q
  37. Point(b) → J
  38. Ray(C, J) → r