MathPlotAI Logo MathPlotAI

Dynamic Illustration of a Theorem Involving 2 Circles and 2 Chords

Dynamic Illustration of a Theorem Involving 2 Circles and 2 Chords
Loading the math board and drawing, please wait…
2017-03-27 16:55
CircleVectorGeometric Construction
In collections Circles (Theorems)
This example dynamically illustrates a theorem involving two circles and two chords. It uses various GeoGebra commands such as Circle, Segment, PointIn, Line, Intersect, Point, CircleSector, Dilate, Ray, Angle, Rotate, Vector, and Translate to construct a modifiable illustration. Suitable for students at the junior high school level and above to learn geometric transformations and theorem proofs.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. PointIn(a) → C
  4. Line(A, C) → g
  5. Intersect(c, g, 2) → D
  6. Intersect(c, g, 1) → E
  7. Segment(C, D) → h
  8. Segment(C, E) → i
  9. Circle(C, b) → d
  10. Intersect(d, c) → F, G, ,
  11. Point(c) → H
  12. Point(c) → I
  13. Line(H, G) → j
  14. Intersect(d, j) → J, K
  15. Line(I, F) → k
  16. Intersect(d, k, 2) → L
  17. Segment(H, I) → l
  18. Segment(K, L) → m
  19. Circle(H, (0.3 * Min[l, m])) → e
  20. Intersect(e, l, 1) → M
  21. Intersect(e, j, 2) → N
  22. CircleSector(H, M, N) → p
  23. Dilate(H, If[0 < n ≤ 1, 1 - n, 0], G) → H'
  24. Segment(H, H') → q
  25. Dilate(G, If[1 < n ≤ 2, 2 - n, 0], K) → G'
  26. Segment(G, G') → r
  27. Circle(K, 1) → s
  28. Intersect(s, j, 2) → O
  29. Ray(K, O) → t
  30. Dilate(I, If[2 < n ≤ 3, 3 - n, 0], F) → I'
  31. Segment(I, I') → f_1
  32. Dilate(F, If[3 < n ≤ 4, 4 - n, 0], L) → F'
  33. Segment(F, F') → g_1
  34. Dilate(I, If[4 < n ≤ 5, 5 - n, 0], H) → I'_1
  35. Dilate(L, If[4 < n ≤ 5, 5 - n, 0], K) → L'
  36. Segment(I, I'_1) → h_1
  37. Segment(L, L') → i_1
  38. Angle(M, H, N) → α
  39. Rotate(M, If[5 < n ≤ 6, ((n - 5) * α), α], H) → M'
  40. CircleSector(H, M, M') → c_1
  41. Dilate(H, If[6.5 < n ≤ 7.5, 7.5 - n, 0], K) → H'_1
  42. Vector(H, H'_1) → u
  43. Translate(p, u) → d_1