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Animation of Circle and Tangent Line

Animation of Circle and Tangent Line
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2017-03-26 23:04
CircleTransformationGeometric ConstructionSlider Animation
In collections Circle - Area & Circumference
This example demonstrates the relationship between a circle and a tangent line. Key mathematical concepts include circles, tangent lines, and reflections. Using GeoGebra commands such as Circle, Tangent, Angle, and Dilate, the interaction between a point on the circle and the tangent line is dynamically illustrated. Suitable for high school mathematics education, particularly in coordinate geometry and calculus courses.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. Segment(A, C) → g
  4. Point(g) → D
  5. Circle(D, C) → d
  6. Point(d) → E
  7. Line(D, E) → h
  8. OrthogonalLine(E, h) → i
  9. Line(C, E) → j
  10. Intersect(c, j, 2) → F
  11. Tangent(F, c) → k,
  12. Segment(A, F) → l
  13. Segment(D, E) → m
  14. Circle(E, a) → e
  15. Circle(F, a) → p
  16. Intersect(p, k) → G, H
  17. Intersect(e, i) → I, J
  18. Intersect(p, l, 1) → K
  19. Intersect(e, m, 1) → L
  20. Angle(G, F, K) → α
  21. Angle(J, E, L) → β
  22. Intersect(e, j, 1) → M
  23. Intersect(p, j, 1) → N
  24. CircleSector(E, M, I) → q
  25. Dilate(D, If[0 < b ≤ 1, 1 - b, 0], E) → D'
  26. Segment(D, D') → n
  27. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], F) → A'
  28. Segment(A, A') → r
  29. Angle(M, E, I) → γ
  30. Rotate(M, If[4 < b ≤ 5, ((b - 4) * γ), γ], E) → M'
  31. CircleSector(E, M, M') → s
  32. Dilate(E, If[5.5 < b ≤ 6.5, 6.5 - b, 0], F) → E'
  33. Vector(E, E') → u
  34. Dilate(C, If[2 < b ≤ 3, 3 - b, 0], E) → C'
  35. Segment(C, C') → t
  36. Dilate(E, If[3 < b ≤ 4, 4 - b, 0], F) → E'_1
  37. Segment(E, E'_1) → f_1
  38. Translate(q, u) → s'

AI Drawing Prompt Reference

Draw a circle with a tangent line at a point on the circle. From a point on the tangent, construct a perpendicular line. Connect the circle center to the tangency point. At the tangency point, create two small circles of equal radius intersecting the tangent and the perpendicular. Use a slider to animate: the tangency point moves along the circle, the tangent updates, and segments from the center and tangent point are shown. Also display sectors formed by these points and a translated sector via a vector, all dynamically scaled by the slider.
The prompt above was compiled from the original drawing commands and is for reference only.