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Exploring the Circumcenter

Exploring the Circumcenter
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2019-11-01 20:27
TriangleCircleGeometric ConstructionLocus
This example demonstrates how the circumcenter of a triangle moves as its vertices are manipulated. Key concepts include circumcenter, perpendicular bisectors, triangles, and circles. Constructed using commands like Polygon, LineBisector, Intersect, Circle, and Segment. Ideal for high school geometry instruction to investigate properties of the circumcenter and its relation to the triangle.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(c) → d
  3. LineBisector(b) → e
  4. LineBisector(a) → f
  5. Intersect(d, e) → Circumcenter
  6. Circle(Circumcenter, C) → g
  7. Intersect(a, f) → E
  8. Intersect(e, b) → F
  9. Intersect(d, c) → G
  10. Segment(A, G) → h
  11. Segment(G, B) → i
  12. Segment(B, E) → j
  13. Segment(E, C) → k
  14. Segment(C, F) → l
  15. Segment(F, A) → m
  16. Intersect(g, e) → D, H
  17. Intersect(g, d) → I, J
  18. Intersect(g, f) → K, L
  19. Angle(L, E, B) → α
  20. Angle(A, F, H) → β
  21. Angle(J, G, A) → γ