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The Four Centers of a Triangle

The Four Centers of a Triangle
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2013-10-05 04:42
TriangleCircleCoordinate Geometry
This example demonstrates the effect of changing a triangle's shape on its circumcenter (and circumcircle), incenter (and incircle), and centroid (and medians). Using GeoGebra commands such as Polygon, LineBisector, Intersect, etc., you can observe these geometric elements changing. Suitable for middle school and above students to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(c) → d
  3. LineBisector(b) → e
  4. LineBisector(a) → f
  5. Intersect(d, f) → D
  6. AngularBisector(c, b) → g, h
  7. AngularBisector(b, a) → i, j
  8. AngularBisector(a, c) → k, l
  9. Intersect(l, h) → E
  10. Circle(D, B) → p
  11. OrthogonalLine(E, c) → m
  12. Intersect(c, m) → F
  13. Circle(E, F) → q
  14. Intersect(d, c) → G
  15. Intersect(f, a) → H
  16. Intersect(e, b) → I
  17. Segment(B, I) → r
  18. Segment(C, G) → s
  19. Segment(A, H) → t
  20. Intersect(t, r) → J
  21. OrthogonalLine(C, c) → a_1
  22. OrthogonalLine(A, a) → b_1
  23. OrthogonalLine(B, b) → c_1
  24. Intersect(a_1, b_1) → K
  25. Line(K, J) → d_1