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Circumcenter Geometric Construction

Circumcenter Geometric Construction
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2017-05-09 22:35
TriangleCircleGeometric Construction
In collections Centers of Triangles
This example demonstrates how to find the circumcenter of a triangle by constructing the perpendicular bisectors of its three sides. Key mathematical concepts include perpendicular bisectors, midpoints, intersection points, circles, and basic properties of triangles. The construction involves using GeoGebra commands such as Segment, Midpoint, OrthogonalLine, Intersect, and Circle. It is suitable for high school mathematics education, helping students understand the definition and properties of the circumcenter and mastering basic geometric construction techniques.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Midpoint(f) → D
  5. Midpoint(h) → E
  6. Midpoint(g) → F
  7. OrthogonalLine(D, f) → i
  8. OrthogonalLine(F, g) → j
  9. OrthogonalLine(E, h) → k
  10. Intersect(i, j) → G
  11. Angle(C, A, B) → α
  12. Circle(G, B) → c