三角形的心与圆

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Midpoint(c) → M_C
3. Midpoint(a) → M_A
4. Midpoint(b) → M_B
5. Segment(M_C, C) → f
6. Segment(B, M_B) → g
7. Segment(A, M_A) → h
8. Intersect(f, g) → centroid
9. LineBisector(c) → j
10. LineBisector(a) → k
11. LineBisector(b) → l
12. Intersect(j, k) → circumcentre
13. Angle(C, M_B, circumcentre) → α
14. Angle(A, M_C, circumcentre) → β
15. Angle(B, M_A, circumcentre) → γ
16. Segment(A, M_C) → m
17. Segment(M_C, B) → n
18. Segment(A, M_B) → p
19. Segment(M_B, C) → q
20. Segment(C, M_A) → r
21. Segment(M_A, B) → s
22. AngularBisector(C, A, B) → f_1
23. AngularBisector(A, B, C) → g_1
24. AngularBisector(B, C, A) → h_1
25. Intersect(h_1, f_1) → incentre
26. Angle(C, A, incentre) → δ
27. Angle(incentre, A, B) → ε
28. Angle(A, B, incentre) → ζ
29. Angle(incentre, B, C) → η
30. Angle(B, C, incentre) → θ
31. Angle(incentre, C, A) → ι
32. OrthogonalLine(incentre, c) → i_1
33. Intersect(i_1, c) → D
34. Circle(incentre, D) → incircle
35. Circle(A, B, C) → d_1
36. Angle(A, D, incentre) → κ
37. Segment(circumcentre, B) → r_1
38. Segment(circumcentre, A) → r_2
39. Segment(circumcentre, C) → r_3
40. OrthogonalLine(C, c) → alt_1
41. OrthogonalLine(A, a) → alt_2
42. Intersect(alt_1, c) → F
43. Intersect(a, alt_2) → G
44. Distance(circumcentre, centroid) → distancecircumcentrecentroid
45. OrthogonalLine(B, b) → alt_3
46. Intersect(b, alt_3) → E
47. Angle(B, E, A) → λ
48. Intersect(alt_1, alt_3) → orthocentre
49. Angle(A, F, orthocentre) → μ
50. Angle(B, G, orthocentre) → ν
51. Segment(circumcentre, centroid) → j_1
52. Segment(centroid, orthocentre) → k_1