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Orthocenter Mirror and Circle Concurrency

Orthocenter Mirror and Circle Concurrency
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2015-10-22 00:42
TriangleCircleCoordinate GeometryTransformationGeometric Construction
This example demonstrates the concurrency of the orthocenter's mirror image and points on the circumcircle of a triangle. Key mathematical concepts include orthocenter, coordinates, special points, and conic sections. Using GeoGebra commands such as Polygon, OrthogonalLine, Circle, Intersect, Mirror, and Prove, the construction of the orthocenter and its mirror image points, and the proof of their concurrency with the circumcircle are shown. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(B, b) → e
  4. Circle(A, B, C) → f
  5. Intersect(e, d) → D
  6. Mirror(D, a) → D'
  7. Prove(AreConcyclic[A, B, C, D']) → g

AI Drawing Prompt Reference

Draw a triangle, find its orthocenter, then reflect the orthocenter to get its mirror image, draw the circumcircle of the triangle, and prove that the mirror image of the orthocenter and the three points on the circumcircle are concurrent.
The prompt above was compiled from the original drawing commands and is for reference only.