九点圆与欧拉线：三角形几何中的重要概念

GeoGebra 命令及参数

1. Line(A, B) → m
2. Line(C, A) → n
3. Line(B, C) → q
4. OrthogonalLine(A, q) → a
5. OrthogonalLine(B, n) → b
6. OrthogonalLine(C, m) → c
7. Intersect(a, b) → H
8. LineBisector(B, C) → d
9. LineBisector(C, A) → e
10. LineBisector(A, B) → f
11. Intersect(d, e) → O
12. Mirror(O, n) → O'_3
13. Mirror(O, q) → O'_1
14. Mirror(O, m) → O'_2
15. Mirror(H, m) → H'_3
16. Mirror(H, n) → H'_1
17. Mirror(H, q) → H'_2
18. Circle(H'_3, H'_1, H'_2) → g
19. Circle(O'_2, O'_3, O'_1) → h
20. Intersect(q, a) → D
21. Intersect(n, e) → E
22. Intersect(n, b) → F
23. Intersect(m, c) → G_1
24. Intersect(m, f) → I
25. Intersect(q, d) → J
26. Circle(G_1, D, E) → k
27. Midpoint(H, O) → N
28. Segment(A, J) → i
29. Segment(B, E) → j
30. Segment(I, C) → l
31. Intersect(i, j) → G
32. Line(H, O) → r
33. Mirror(H, O) → L