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Dynamic Illustration of a Special Secant Segment in Intersecting Circles

Dynamic Illustration of a Special Secant Segment in Intersecting Circles
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2017-05-23 19:55
CircleGeometric Construction
This example dynamically illustrates the drawing and modification of a special secant segment within two intersecting circles at two distinct points. It involves core mathematical concepts such as circles, intersecting lines, chord lengths, and dynamic geometric transformations. The construction utilizes GeoGebra commands and objects like Circle, Segment, PointIn, Distance, Line, Intersect, CircleArc, Point, Midpoint, Dilate, and Rotate. It is suitable for high school students and teachers studying analytical geometry, geometric transformations, and dynamic geometry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. PointIn(a) → C
  4. Distance(C, c) → b
  5. Line(A, C) → g
  6. Intersect(c, g, 2) → D
  7. Intersect(c, g, 1) → E
  8. Distance(C, D) → d
  9. Distance(C, E) → e
  10. Circle(C, h) → k
  11. Intersect(k, c) → F, G, ,
  12. CircleArc(A, G, F) → p
  13. Point(p) → H
  14. Line(H, G) → i
  15. Intersect(k, i) → I, J
  16. Midpoint(A, C) → K
  17. Circle(K, G) → q
  18. Line(H, G) → j
  19. Intersect(q, j) → L, M
  20. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], K) → A'
  21. Segment(A, A') → m
  22. Dilate(K, If[1 < l ≤ 2, 2 - l, 0], C) → K'
  23. Segment(K, K') → n
  24. Rotate(A, If[2 < l ≤ 3, ((l - 2) * π), π], K) → A'_1
  25. Rotate(A', If[2 < l ≤ 3, ((l - 2) * π), π], K) → A''
  26. Segment(A'_1, A'') → m'
  27. Dilate(K, If[3 < l ≤ 4, 4 - l, 0], G) → K'_1
  28. Segment(K, K'_1) → r
  29. Rotate(K, If[4 < l ≤ 6, ((l - 4) * π), (2 * π)], K) → K'_2
  30. Rotate(K'_1, If[4 < l ≤ 6, ((l - 4) * π), (2 * π)], K) → N
  31. Segment(K'_2, N) → r'
  32. CircleArc(K, G, N) → s
  33. Dilate(H, If[6 < l ≤ 7, 7 - l, 0], M) → H'_1
  34. Segment(H, H'_1) → t
  35. Dilate(M, If[7 < l ≤ 8, 8 - l, 0], J) → M'
  36. Segment(M, M') → f_1
  37. Rotate(H, If[8 < l ≤ 9, ((l - 8) * π), π], M) → H'
  38. Rotate(H'_1, If[8 < l ≤ 9, ((l - 8) * π), π], M) → O
  39. Segment(H', O) → t'