三角形的垂心、重心与外心及欧拉线探究

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Segment(B, C) → g
3. Segment(C, A) → h
4. Line(A, B) → i
5. Line(B, C) → j
6. Line(C, A) → k
7. Polygon(A, B, C) → poly1, c, a, b
8. OrthogonalLine(C, i) → l
9. OrthogonalLine(A, j) → m
10. OrthogonalLine(B, k) → n
11. Intersect(l, m) → D
12. Midpoint(C, B) → F
13. Midpoint(A, B) → G
14. Midpoint(A, C) → H
15. Segment(A, F) → p
16. Segment(C, G) → q
17. Segment(B, H) → r
18. Intersect(q, r) → I
19. OrthogonalLine(G, f) → s
20. OrthogonalLine(F, j) → t
21. OrthogonalLine(H, h) → d
22. Intersect(d, s) → J
23. Intersect(i, l) → E
24. Intersect(j, m) → K
25. Angle(C, K, A) → α
26. Point(i) → L
27. Angle(C, E, L) → β
28. Intersect(k, n) → M
29. Angle(B, M, A) → γ
30. Angle(J, G, A) → δ
31. Point(t) → N
32. Angle(C, F, N) → ε
33. Angle(J, H, C) → ζ
34. Dilate(J, If[0 < v ≤ 1, 1 - v, 0], I) → J'
35. Midpoint(I, D) → O
36. Segment(J, J') → f_1
37. Dilate(I, If[1 < v ≤ 2, 2 - v, 0], O) → I'
38. Segment(I, I') → g_1
39. Dilate(O, If[2 < v ≤ 3, 3 - v, 0], D) → O'
40. Segment(O, O') → h_1
41. Rotate(J, If[3 < v ≤ 4, ((-(v - 3)) * π), (-π)], I) → J'_1
42. Rotate(J', If[3 < v ≤ 4, ((-(v - 3)) * π), (-π)], I) → J''
43. Segment(J'_1, J'') → i_1
44. Rotate(J'_1, If[4 < v ≤ 5, ((-(v - 4)) * π), (-π)], O) → P
45. Rotate(J'', If[4 < v ≤ 5, ((-(v - 4)) * π), (-π)], O) → J'''
46. Segment(P, J''') → j_1