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Circumcenter of a Triangle by Sarah Marsh

Circumcenter of a Triangle by Sarah Marsh
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2016-10-10 09:21
TriangleCircleGeometric Construction
In collections Points of Concurrency in a Triangle
This example demonstrates the construction of the circumcenter of a triangle by intersecting the angle bisectors. It involves core concepts like angle bisectors, intersection points, circles, and triangle geometry. GeoGebra commands used include Polygon, LineBisector, Intersect, Circle, Segment. Suitable for high school geometry education and construction learning.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a triangle ABC, then draw the angle bisectors AD, BE, and CF. Find the intersection point D of these bisectors. Next, draw circles centered at D that are tangent to the sides of the triangle. Finally, connect D to the three vertices of the triangle to form three circles corresponding to the central angles.
The prompt above was compiled from the original drawing commands and is for reference only.