内切圆、外接圆、Gergonne点与Nagel点

GeoGebra 命令及参数

1. Line(A, B) → f
2. Line(B, C) → g
3. Line(C, A) → h
4. AngularBisector(f, h) → i, j
5. AngularBisector(h, g) → k, l
6. AngularBisector(g, f) → m, n
7. Intersect(i, l) → E_C
8. Intersect(j, l) → I
9. Intersect(i, k) → E_B
10. Intersect(j, k) → E_A
11. OrthogonalLine(I, g) → p
12. OrthogonalLine(E_A, g) → q
13. Intersect(g, p) → G
14. Circle(I, G) → c
15. Intersect(g, q) → I_{1}
16. Circle(E_A, I_{1}) → d
17. OrthogonalLine(E_B, h) → r
18. OrthogonalLine(E_C, f) → s
19. Intersect(h, r) → J
20. Circle(E_B, J) → e
21. Intersect(f, s) → K
22. Circle(E_C, K) → t
23. Polygon(A, B, C) → t1, c_1, a, b
24. Midpoint(B, C) → D
25. Midpoint(C, A) → E
26. Midpoint(A, B) → F
27. Intersect(f, c_1) → H
28. Intersect(c, f) → C', R
29. Intersect(h, b) → M
30. Intersect(h, b) → N
31. Intersect(c, h) → O, B'
32. Intersect(c, g) → P, A'
33. Segment(A, A') → f_1
34. Segment(C', C) → g_1
35. Segment(B', B) → h_1
36. Intersect(f_1, g_1) → G_e