MathPlotAI Logo MathPlotAI

Dynamic Illustration of Median & Circles

Dynamic Illustration of Median & Circles
Loading the math board and drawing, please wait…
2020-11-22 20:27
TriangleCircleGeometric ConstructionLocus
This example dynamically illustrates a not-often-seen theorem involving a triangle's median and two circles. It covers core math concepts like medians, circles, and geometric transformations. Construction uses commands such as Polygon, Segment, Midpoint, Dilate, Rotate, Point, Circle, Line, Intersect, Ray, Angle, and CircleArc. Suitable for high school and above students to understand geometric transformations and theorem applications.

GeoGebra Commands & Parameters

  1. Polygon(A, C, B) → poly1, c, a, b
  2. Segment(B, A) → f
  3. Segment(B, C) → g
  4. Midpoint(A, C) → M
  5. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], M) → A'
  6. Segment(A, A') → h
  7. Rotate(A, If[1 < d ≤ 2, ((d - 1) * π), π], M) → A'_1
  8. Rotate(A', If[1 < d ≤ 2, ((-(d - 1)) * π), (-π)], M) → A''
  9. Segment(A'_1, A'') → h'
  10. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], M) → C'
  11. Segment(B, C') → i
  12. Segment(B, M) → j
  13. Segment(A, C) → k
  14. Point(k) → D
  15. Midpoint(D, A) → E
  16. Segment(A, C) → l
  17. Circle(E, D) → e
  18. Midpoint(D, C) → F
  19. Circle(F, D) → p
  20. Line(B, D) → m
  21. Intersect(e, m, 2) → G
  22. Intersect(p, m, 2) → H
  23. Segment(M, G) → n
  24. Segment(M, H) → q
  25. Circle(B, 1) → r
  26. Circle(H, 1) → s
  27. Intersect(s, m, 2) → J
  28. Intersect(r, m, 1) → K
  29. Ray(H, J) → t
  30. Ray(B, K) → f_1
  31. Dilate(B, If[4 < d ≤ 5, 5 - d, 0], D) → B'
  32. Segment(B, B') → g_1
  33. Angle(D, E, G) → α
  34. Angle(C, F, H) → β
  35. Rotate(D, If[5 < d ≤ 6, ((d - 5) * α), α], E) → D'
  36. CircleArc(E, D, D') → c_1
  37. Rotate(G, If[6 < d ≤ 7, ((d - 6) * ((2 * π) - α)), (2 * π) - α], E) → D'_1
  38. CircleArc(E, G, D'_1) → d_1
  39. Rotate(C, If[7 < d ≤ 8, ((d - 7) * β), β], F) → C'_1
  40. CircleArc(F, C, C'_1) → e_1
  41. Rotate(H, If[8 < d ≤ 9, ((d - 8) * ((2 * π) - β)), (2 * π) - β], F) → H'
  42. CircleArc(F, H, H') → k_1
  43. Angle(H, M, G) → γ
  44. Dilate(M, If[9 < d ≤ 10, 10 - d, 0], H) → M'
  45. Segment(M, M') → i_1
  46. Dilate(M, If[10 < d ≤ 11, 11 - d, 0], G) → M'_1
  47. Segment(M, M'_1) → j_1
  48. Rotate(M, If[11 < d ≤ 12, ((-(d - 11)) * ((2 * π) - γ)), (-((2 * π) - γ))], M) → M'_2
  49. Rotate(M', If[11 < d ≤ 12, ((-(d - 11)) * ((2 * π) - γ)), (-((2 * π) - γ))], M) → M''
  50. Segment(M'_2, M'') → l_1
  51. Ray(B, D) → h_1
  52. Point(h_1) → I
  53. Ray(D, I) → m_1

AI Drawing Prompt Reference

Draw a triangle with a midpoint on one side. From this midpoint, create a dynamic segment whose length varies with a parameter, and rotate and scale the triangle's vertices around the midpoint to form auxiliary points. Pick a point on one side, and construct two circles centered at the midpoints between this point and the side's endpoints. Mark the intersections of these circles with the median line. Connect the midpoint to these intersections with segments. Then draw small circles centered at a vertex and a point, and construct rays. Finally, use rotations and dilations to create arcs and angles, illustrating the geometric relationship between the median and the circles.
The prompt above was compiled from the original drawing commands and is for reference only.