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Notable Points of a Triangle

Notable Points of a Triangle
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2012-02-07 20:54
TriangleCircleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the significant points of triangle ABC: circumcenter, incenter, orthocenter, and barycenter. It involves core math concepts like circles, angles, trigonometry, and geometric constructions. Constructed using commands such as Circle, Point, Polygon, Center, Line, OrthogonalLine, Intersect, AngularBisector, Locus. Suitable for high school and above students exploring geometric properties.

GeoGebra Commands & Parameters

  1. Circle(D, E) → c
  2. Point(c) → C
  3. Polygon(A, B, C) → polígono1, c_1, a, b
  4. Circle(A, B, C) → d
  5. Center(d) → circun
  6. Line(bari, circun) → e
  7. OrthogonalLine(A, a) → f
  8. OrthogonalLine(B, b) → g
  9. Intersect(g, f) → orto
  10. AngularBisector(B, A, C) → h
  11. AngularBisector(A, C, B) → i
  12. Intersect(i, h) → in
  13. Locus(circun, C) → lgcircun
  14. Locus(bari, C) → lgbari
  15. Locus(orto, C) → lgor
  16. Locus(in, C) → lgincentro

AI Drawing Prompt Reference

Draw triangle ABC, then construct its circumcenter, incenter, orthocenter, and centroid in sequence. First, draw the circumcircle and find the circumcenter; then draw the angle bisectors to find the incenter; construct perpendicular lines to find the orthocenter; finally, use the properties of the centroid to find it.
The prompt above was compiled from the original drawing commands and is for reference only.