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Perpendicular Bisectors Concurrency - Circumcenter

Perpendicular Bisectors Concurrency - Circumcenter
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2015-11-26 07:01
TriangleCircleCoordinate Geometry
In collections Points of Concurrency of Triangles
This GeoGebra worksheet demonstrates that the perpendicular bisectors of a triangle are concurrent at a single point, known as the circumcenter. Key concepts include the circumcenter, perpendicular bisectors, and circles. Using commands like Polygon, LineBisector, and Intersect, the construction of the circumcenter is illustrated. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(a) → d
  3. LineBisector(b) → e
  4. LineBisector(c) → f
  5. Intersect(e, f) → D
  6. Angle(C, A, B) → α
  7. Angle(A, C, B) → β
  8. Angle(A, B, C) → γ
  9. Angle(e, b) → δ
  10. Angle(f, c) → ε
  11. Angle(a, d) → ζ
  12. Angle(A, B, C) → η
  13. Intersect(e, b) → F
  14. Intersect(a, d) → E
  15. Intersect(c, f) → G
  16. Segment(A, G) → h
  17. Segment(G, B) → i
  18. Segment(B, E) → j
  19. Segment(E, C) → k
  20. Segment(C, F) → l
  21. Segment(F, A) → m
  22. Intersect(f, c) → H
  23. Intersect(a, d) → I
  24. Intersect(b, e) → J
  25. Segment(A, H) → n
  26. Segment(H, B) → p
  27. Segment(B, I) → q
  28. Segment(I, C) → r
  29. Segment(J, C) → s
  30. Segment(A, J) → t
  31. Angle(n, q) → θ
  32. Intersect(r, s) → K
  33. Segment(B, D) → a_1
  34. Segment(D, C) → b_1
  35. Segment(D, A) → c_1
  36. Circle(D, B) → d_1