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Excenter

Excenter
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2014-11-24 06:27
TriangleAngleGeometric Construction
This example demonstrates the concept of an excenter, which is the intersection of the external angle bisectors of a triangle. Using GeoGebra commands such as Polygon, Line, AngularBisector, Point, and Intersect, one can construct a triangle and its excenter. Suitable for middle school and above students to learn about triangle properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(B, A) → d
  3. Line(B, C) → e
  4. AngularBisector(A, B, C) → f
  5. Point(d) → D
  6. Point(e) → E
  7. AngularBisector(C, A, D) → g
  8. AngularBisector(E, C, A) → h
  9. Intersect(f, g) → F
  10. OrthogonalLine(F, b) → i
  11. Intersect(i, b) → G
  12. Circle(F, G) → k

AI Drawing Prompt Reference

Draw a triangle and its two external angle bisectors, their intersection is the excenter. Then, draw perpendiculars from the vertices to the opposite sides to find the feet of the altitudes. Draw a circle with the feet of the altitudes as centers, and find the intersection points with the external angle bisectors. Connect these points to the vertices to complete the construction.
The prompt above was compiled from the original drawing commands and is for reference only.