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Dynamic Illustration of Tangent Circles, Tangents, and Secant

Dynamic Illustration of Tangent Circles, Tangents, and Secant
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2017-03-26 21:38
CircleTrigonometryGeometric Construction
In collections Circles (Theorems)
This example dynamically illustrates the geometric relationships involving two mutually tangent circles, their tangents, and a secant line passing through a point of tangency. Key mathematical concepts include properties of tangent lines, the secant theorem, angle relationships, and dynamic geometric transformations. The construction utilizes commands such as Circle, Segment, Point, Line, OrthogonalLine, Intersect, Tangent, Angle, CircleSector, Dilate, Rotate, Vector, and Translate. It is suitable for high school geometry instruction, conic sections exploration, and dynamic geometry investigations.

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'