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Locus of the Centroid of a Triangle

Locus of the Centroid of a Triangle
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2015-03-24 00:24
TriangleCircleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the locus of the centroid G of a triangle as vertex A moves along a circular arc. Key math concepts include medians, centroid, locus, and coordinate geometry. Construction involves commands like Circle, Point, Segment, Midpoint, and Intersect. Suitable for high school students and above to explore geometric dynamic properties and centroid characteristics.

GeoGebra Commands & Parameters

  1. Circle(T, L) → c
  2. Point(c) → A
  3. Point(c) → B
  4. Point(c) → C
  5. Segment(A, C) → a
  6. Segment(C, B) → b
  7. Segment(B, A) → d
  8. Midpoint(b) → D
  9. Midpoint(d) → E
  10. Midpoint(a) → F
  11. Segment(A, D) → e
  12. Segment(C, E) → f
  13. Segment(B, F) → g
  14. Intersect(e, f) → G
  15. Segment(A, E) → h
  16. Segment(E, B) → i
  17. Segment(B, D) → j
  18. Segment(D, C) → k
  19. Segment(C, F) → l
  20. Segment(F, A) → m