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Points of Intersection 18

Points of Intersection 18
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2016-03-27 07:10
CircleCoordinate GeometryGeometric Construction
This example demonstrates the calculation and geometric properties of intersections among polygons, line segments, and circles. It involves core math concepts like coordinate geometry, geometric construction, incircles of polygons, and intersection points. Constructed using commands such as Polygon, Point, Line, Intersect, Segment, Incircle, Center. Suitable for high school mathematics teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(c) → D
  3. Line(D, a) → d
  4. Line(D, b) → e
  5. Intersect(d, b) → E
  6. Line(E, c) → f
  7. Intersect(f, a) → F
  8. Intersect(e, a) → G
  9. Line(F, b) → g
  10. Line(G, c) → h
  11. Intersect(g, c) → H
  12. Intersect(h, b) → I
  13. Segment(D, E) → i
  14. Segment(E, F) → j
  15. Segment(F, H) → k
  16. Segment(H, I) → l
  17. Segment(I, G) → m
  18. Segment(G, D) → n
  19. Intersect(n, l) → J
  20. Intersect(j, n) → K
  21. Intersect(l, j) → L
  22. Incircle(A, D, E) → p
  23. Incircle(H, D, J) → q
  24. Incircle(B, H, F) → r
  25. Incircle(F, K, G) → s
  26. Incircle(G, C, I) → t
  27. Incircle(I, L, E) → c_1
  28. Center(p) → M
  29. Center(q) → N
  30. Center(r) → O
  31. Center(s) → P
  32. Center(c_1) → Q
  33. Center(t) → R
  34. Segment(M, P) → a_1
  35. Segment(O, Q) → b_1
  36. Segment(N, R) → d_1
  37. Intersect(a_1, d_1) → S