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Orthocenter and Circumcenter Proof

Orthocenter and Circumcenter Proof
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2016-02-05 23:25
TriangleVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates and proves the relationship between the orthocenter and circumcenter of a triangle. It involves core mathematical concepts like vectors, trigonometry, and coordinate geometry. The construction utilizes GeoGebra commands such as Polygon, Circle, OrthogonalLine, Intersect, Center, Distance, Line, and Segment. Suitable for high school and above mathematics learners to understand key geometric properties of triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B_1, C) → poly1, c, a, b
  2. Circle(A, B_1, C) → d
  3. OrthogonalLine(A, a) → e
  4. OrthogonalLine(B_1, b) → f
  5. Intersect(e, f) → H
  6. Center(d) → O
  7. OrthogonalLine(O, a) → g
  8. Intersect(g, a) → D
  9. Distance(A, H) → distanceAH
  10. Distance(O, D) → distanceOD
  11. Line(O, B_1) → h
  12. Intersect(d, h) → E, F
  13. Line(H, C) → i
  14. Segment(F, A) → j
  15. Segment(F, C) → k
  16. Intersect(i, c) → N