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Incenter, Excenter, Orthocenter

Incenter, Excenter, Orthocenter
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2015-10-22 05:11
TriangleAngleGeometric Construction
This example demonstrates the incenter, excenter, and orthocenter of a triangle. Key mathematical concepts include angle bisectors, external angle bisectors, altitudes, and circles. Using GeoGebra commands such as Polygon, AngularBisector, Intersect, OrthogonalLine, Circle, and Segment, the incenter, excenter, and orthocenter of a triangle can be constructed. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a triangle and construct its angle bisectors, their intersection point being the incenter. Then draw perpendiculars from the incenter to the three sides, meeting the sides at the feet of the altitudes. Next, construct the external angle bisectors, intersecting the circumcircle at three points, and connect these points to form the excircle. Finally, connect the incenter to the feet of the altitudes to form the incircle and its radius.
The prompt above was compiled from the original drawing commands and is for reference only.