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Angle Center Constructions 1

Angle Center Constructions 1
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2017-10-05 20:15
TriangleCircleGeometric Construction
This example demonstrates the construction methods and properties of angle centers (e.g., incenter, circumcenter) in geometry. It involves core math concepts like triangles, circles, polygons, angles, and geometric constructions. Key GeoGebra commands/objects used include Polygon, Point, Circle, Intersect, Segment, Distance, and Midpoint, as summarized. Suitable for high school mathematics teaching or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Point(a) → D
  3. Circle(C, Segment[C, D]) → d
  4. Circle(B, Segment[C, D]) → e
  5. Intersect(d, e, 1) → E
  6. Intersect(d, e, 2) → F
  7. Segment(E, F) → f
  8. Intersect(a, f) → G
  9. Distance(G, C) → distanceGC
  10. Distance(G, B) → distanceGB
  11. Point(b) → H
  12. Circle(C, Segment[H, C]) → g
  13. Circle(A, Segment[H, C]) → h
  14. Intersect(g, h, 2) → I
  15. Intersect(g, h, 1) → J
  16. Segment(I, J) → i
  17. Intersect(i, b) → K
  18. Distance(K, C) → distanceKC
  19. Distance(K, A) → distanceKA
  20. Point(c) → L
  21. Circle(B, Segment[L, B]) → k
  22. Circle(A, Segment[L, B]) → p
  23. Intersect(k, p, 1) → M
  24. Intersect(k, p, 2) → N
  25. Segment(M, N) → j
  26. Intersect(c, j) → O
  27. Distance(O, A) → distanceOA
  28. Distance(O, B) → distanceOB
  29. Intersect(j, f) → P
  30. Intersect(k, p) → Q, R, ,
  31. Distance(P, B) → distancePB
  32. Midpoint(P, B) →
  33. Distance(P, K) → distancePK
  34. Midpoint(P, K) →