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Interactive Exploration of Marion's Theorem

Interactive Exploration of Marion's Theorem
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2026-10-26 23:59
TriangleCircleGeometric Construction
In collections Euclidean Geometry
This example explores Marion's theorem for triangles through interactive means. It demonstrates the relationship between the incircle and the sides of a triangle, involving concepts such as triangles and incircles. It uses commands like Point, Mirror, and Polygon for construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → PEEPST
  2. Mirror(PP1, yAxis) → PP2
  3. Mirror(PP2, xAxis) → PP3
  4. Polygon({PP1, PP2, PP3, PP4}) → peep
  5. PointIn(peep) → A
  6. PointIn(peep) → B
  7. PointIn(peep) → C
  8. Polygon({A, B, C}) → givenTri
  9. Segment(B, B') → segmBBP
  10. Segment(B, B'') → segmBBS
  11. Segment(A, A') → segmAAP
  12. Segment(A, A'') → segmAAS
  13. Segment(C, C'') → segmCCS
  14. Segment(C, C') → segmCCP
  15. Intersect(segmAAP, segmBBS) → L
  16. Intersect(segmAAP, segmCCS) → M
  17. Intersect(segmBBP, segmCCS) → N
  18. Intersect(segmBBP, segmAAS) → P
  19. Intersect(segmCCP, segmAAS) → Q
  20. Intersect(segmCCP, segmBBS) → R
  21. Polygon({L, M, N, P, Q, R}) → marionHex
  22. Segment(A, B) → segmAB
  23. Segment(B, C) → segmBC
  24. Segment(A, C) → segmAC

AI Drawing Prompt Reference

Draw a triangle and its incircle. Then, obtain three points through mirror operations and connect them to form a hexagon. Next, take points on the three sides of the triangle and connect them to the corresponding vertices of the hexagon with line segments. Finally, find the intersection points of these segments and connect them to complete a complex geometric figure.
The prompt above was compiled from the original drawing commands and is for reference only.