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Centroid, Orthocenter, and Circumcenter

Centroid, Orthocenter, and Circumcenter
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2018-11-17 09:33
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the concepts of the centroid, orthocenter, and circumcenter of a triangle. The centroid is the intersection of the three medians, the orthocenter is the intersection of the three altitudes, and the circumcenter is the intersection of the three perpendicular bisectors. Using GeoGebra commands such as Segment, LineBisector, and Intersect, this example provides a visual understanding of these geometric concepts. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Segment(X, Y) → f
  2. Segment(Y, Z) → g
  3. Segment(Z, X) → h
  4. LineBisector(h) → i
  5. LineBisector(f) → j
  6. LineBisector(g) → k
  7. Intersect(i, j) → circumcenter
  8. Midpoint(h) → D
  9. Midpoint(f) → E
  10. Midpoint(g) → F
  11. Segment(E, Z) → l
  12. Segment(D, Y) → m
  13. Segment(F, X) → n
  14. Intersect(l, m) → centroid
  15. OrthogonalLine(Z, f) → p
  16. OrthogonalLine(X, g) → q
  17. OrthogonalLine(Y, h) → r
  18. Intersect(p, q) → orthocenter
  19. Line(orthocenter, centroid) → euler
  20. Point(euler) → A

AI Drawing Prompt Reference

Draw a triangle and its three medians, altitudes, and perpendicular bisectors. Mark the intersection points of these lines as the centroid, orthocenter, and circumcenter of the triangle. Then, connect the centroid and orthocenter, and mark the midpoint of this segment. Finally, draw the segment connecting the orthocenter, centroid, and midpoint, and mark the midpoint of this segment.
The prompt above was compiled from the original drawing commands and is for reference only.