Centers of a Triangle

GeoGebra Commands & Parameters

1. Segment(A, C) → a
2. Segment(C, B) → b
3. Segment(A, B) → c
4. Midpoint(A, C) → D
5. Midpoint(A, B) → E
6. Midpoint(C, B) → F
7. Segment(A, F) → d
8. Segment(D, B) → e
9. Segment(E, C) → f
10. Intersect(d, e) → Centroid
11. OrthogonalLine(B, a) → g
12. OrthogonalLine(A, b) → h
13. OrthogonalLine(C, c) → i
14. Intersect(g, h) → Orthocenter
15. OrthogonalLine(F, b) → j
16. OrthogonalLine(D, a) → k
17. OrthogonalLine(E, c) → l
18. Intersect(j, k) → Circumcenter
19. Angle(C, A, B) → α
20. Angle(A, B, C) → β
21. Angle(B, C, A) → γ
22. Rotate(C, α / 2, A) → C'
23. Angle(C, A, C') → δ
24. Ray(A, C') → m
25. Rotate(B, β / 2, A) → B'
26. Rotate(B, β / 2, A) → B'_1
27. Rotate(A, β / 2, B) → A'
28. Angle(A, B, A') → ε
29. Ray(B, A') → n
30. Rotate(B, γ / 2, C) → B'_2
31. Angle(B, C, B'_2) → ζ
32. Ray(C, B'_2) → p
33. Intersect(m, n) → Incenter
34. Line(Orthocenter, Circumcenter) → Euler
35. Intersect(i, c) → G
36. Intersect(h, b) → H
37. Intersect(g, a) → I
38. Segment(G, I) → q
39. Segment(H, I) → r
40. Segment(H, G) → s
41. OrthogonalLine(Orthocenter, q) → t
42. Intersect(t, q) → J
43. Circle(Orthocenter, J) → c_1
44. Circle(Circumcenter, C) → d_1
45. OrthogonalLine(Incenter, c) → a_1
46. Intersect(a_1, c) → K
47. Circle(Incenter, K) → e_1