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Circumcircle Construction Example

Circumcircle Construction Example
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2018-10-12 23:11
TriangleCircleGeometric Construction
This example demonstrates how to construct the circumcircle of a triangle using its three vertices. Key math concepts include circle, triangle, angle bisector, intersecting lines, segments, angles, and circle construction. GeoGebra commands and objects used in the construction summary are Polygon, LineBisector, Intersect, Segment, Angle, and Circle. Suitable for high school mathematics teaching, explaining the geometric construction method and properties of the circumcircle.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(c) → f
  3. LineBisector(a) → g
  4. Intersect(g, f) → M
  5. Intersect(f, c) → D
  6. Intersect(a, g) → E
  7. Segment(A, D) → h
  8. Segment(D, B) → i
  9. Segment(B, E) → j
  10. Segment(E, C) → k
  11. Segment(M, A) → l
  12. Segment(M, B) → m
  13. Segment(M, C) → n
  14. Angle(M, D, A) → α
  15. Angle(M, E, B) → β
  16. Circle(M, A) → d

AI Drawing Prompt Reference

Draw a triangle ABC, then construct the perpendicular bisectors of sides AB, BC, and CA, which intersect at point M, the center of the circumcircle. Connect M to A, B, and C to form the circumcircle. Pay attention to the relationship between the sides, angles of the triangle, and the circumcircle.
The prompt above was compiled from the original drawing commands and is for reference only.