MathPlotAI Logo MathPlotAI

Animation Demonstrating Circle and Secant Line Geometry

Animation Demonstrating Circle and Secant Line Geometry
Loading the math board and drawing, please wait…
2017-03-20 04:06
CircleFunctionParametric EquationGeometric Construction
This example dynamically illustrates the geometric relationship between a circle and a secant line through animation. It involves core concepts such as circles, secant lines, parametric curves, plane figures, quadratic functions, incircles, and sequences. The construction utilizes GeoGebra commands like Circle, Point, Tangent, Intersect, CircleArc, Segment, Dilate, Angle, and Rotate. It is suitable for high school and advanced learners to explore parametric equations, geometric transformations, and the dynamic behavior of function graphs.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Circle(A, b) → d
  3. Point(c) → D
  4. Tangent(D, d) → f, g
  5. Intersect(d, g) → E
  6. Intersect(d, f) → F
  7. Intersect(c, g, 2) → G
  8. Intersect(c, f, 2) → H
  9. CircleArc(A, H, G) → e
  10. Point(e) → I
  11. Segment(D, I) → h
  12. Intersect(d, h, 1) → J
  13. Intersect(d, h, 2) → K
  14. Dilate(D, If[0 < i ≤ 1, 1 - i, 0], J) → D'
  15. Segment(D, D') → j
  16. Dilate(J, If[1 < i ≤ 2, 2 - i, 0], K) → J'
  17. Segment(J, J') → k
  18. Dilate(K, If[2 < i ≤ 3, 3 - i, 0], I) → K'
  19. Segment(K, K') → l
  20. Angle(K, A, J) → α
  21. Rotate(D, If[3 < i ≤ 4, ((-(i - 3)) * α), (-α)], A) → D'_1
  22. Rotate(D', If[3 < i ≤ 4, ((-(i - 3)) * α), (-α)], A) → D''
  23. Segment(D'_1, D'') → j'
  24. Rotate(D, (-α), J) → D'_2
  25. Rotate(D', (-α), J) → D''_1
  26. Segment(D'_2, D''_1) → j'_1
  27. Angle(K, J, D'_2) → β
  28. Rotate(D'_1, If[4 < i ≤ 5, ((-(i - 4)) * β), (-β)], K) → L
  29. Rotate(D'', If[4 < i ≤ 5, ((-(i - 4)) * β), (-β)], K) → D'''
  30. Segment(L, D''') → j''