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Dynamic Circle and Chord Relationship

Dynamic Circle and Chord Relationship
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2017-05-22 09:02
CircleAngleTransformationGeometric ConstructionSlider Animation
This example dynamically illustrates the relationship among a circle's diameter, chord, and two special segments (T/Y segments). It covers core concepts like circle properties, chords, special segments, angles, midpoints, rotations, and transformations. Construction uses GeoGebra commands such as Circle, Point, Line, Intersect, Semicircle, OrthogonalLine, Dilate, Segment, Angle, Midpoint, and Rotate. Suitable for high school mathematics education to understand circles and geometric transformations.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(C, A) → f
  4. Intersect(c, f, 2) → D
  5. Semicircle(C, D) → d
  6. Semicircle(D, C) → e
  7. Point(e) → E
  8. Point(d) → F
  9. Line(E, F) → g
  10. Intersect(f, g) → G
  11. OrthogonalLine(C, g) → h
  12. Intersect(g, h) → H
  13. OrthogonalLine(D, g) → i
  14. Intersect(g, i) → I
  15. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], D) → C'
  16. Segment(C, C') → j
  17. Dilate(E, If[1 < a ≤ 2, 2 - a, 0], H) → E'
  18. Segment(E, E') → k
  19. Dilate(F, If[1 < a ≤ 2, 2 - a, 0], I) → F'
  20. Segment(F, F') → l
  21. Dilate(I, If[2 < a ≤ 3, 3 - a, 0], G) → I'
  22. Dilate(H, If[2 < a ≤ 3, 3 - a, 0], G) → H'
  23. Segment(H, H') → m
  24. Segment(I, I') → n
  25. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], H) → C'_1
  26. Dilate(D, If[3 < a ≤ 4, 4 - a, 0], I) → D'
  27. Angle(G, H, C) → α
  28. Segment(D, D') → p
  29. Segment(C, C'_1) → q
  30. Midpoint(E, F) → J
  31. Angle(E, I, D) → β
  32. Rotate(E, If[4.5 < a ≤ 5.5, ((a - 4.5) * π), π], J) → E'_1
  33. Rotate(E', If[4.5 < a ≤ 5.5, ((a - 4.5) * π), π], J) → E''
  34. Rotate(E, If[5 < a ≤ 6, ((a - 5) * π), π], J) → E'_2
  35. Rotate(E', If[5 < a ≤ 6, ((a - 5) * π), π], J) → E''_1
  36. Segment(E'_2, E''_1) → k'