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Finding the Circumcenter with Bubble Method

Finding the Circumcenter with Bubble Method
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2020-07-10 02:58
TriangleCircleGeometric Construction
This example demonstrates how to find the circumcenter of a triangle using a bubble method. Key mathematical concepts include the circumcircle of a triangle, properties of circles, and geometric construction. GeoGebra commands used include Min, Polygon, LineBisector, Radius, Circle, Sequence, Intersect, CircleArc, Segment, Rotate. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Min(Max[anim, 0], 1) → d
  2. Polygon(A, B, C) → t1, c, a, b
  3. LineBisector(c) → f
  4. LineBisector(b) → g
  5. LineBisector(a) → h
  6. Radius(Circle[A, B, C]) → r
  7. Circle(A, (d * r)) → e
  8. Sequence(Circle[Element[l1, k], (d * r)], k, 1, 3) → l2
  9. Circle(B, (d * r)) → k
  10. Circle(C, (d * r)) → p
  11. Intersect(p, h) → D, E
  12. Intersect(p, g) → F, G
  13. Intersect(e, f) → H, I
  14. CircleArc(C, D, F) → q
  15. Segment(F, G) → i
  16. Segment(E, D) → j
  17. CircleArc(C, G, E) → s
  18. CircleArc(C, G, F) → t
  19. CircleArc(A, F, G) → c_1
  20. Segment(H, I) → m
  21. CircleArc(A, F, H) → d_1
  22. CircleArc(A, I, G) → e_1
  23. CircleArc(B, H, I) → f_1
  24. CircleArc(B, H, D) → g_1
  25. CircleArc(B, E, I) → h_1
  26. Min(Max[(2 * (anim - 1)), 0], 1) → ro
  27. Intersect(f, g) → J
  28. Min(Max[(2 * (anim - 1.6)), 0], 1) → ro2
  29. Sequence(Segment[Element[l1, k], J], k, 1, 3) → l3
  30. Sequence(Rotate[Element[l3, k], (ro * 360°), Element[l1, k]], k, 1, 3) → l4
  31. Sequence(Rotate[Element[l3, k], (ro2 * 360°), J], k, 1, 3) → l5
  32. Rotate(Element[l3, 1], (ro2 * 360°), J) → n
  33. Rotate(A, (ro2 * 360°), J) → A'
  34. CircleArc(J, A, A') → k_1

AI Drawing Prompt Reference

Draw a triangle and locate its circumcenter. Construct the perpendicular bisectors of all three sides; they intersect at the circumcenter. Using one vertex as the center and the circumradius as the radius, draw a circle. Repeat with the other two vertices. As an animation parameter changes, these circles expand, intersecting the bisectors to create arcs and segments, illustrating the bubble method. Finally, connect the circumcenter to each vertex, and rotate these segments around the vertices or the circumcenter to complete the dynamic construction.
The prompt above was compiled from the original drawing commands and is for reference only.