关于三角形重心的一个有趣猜想

GeoGebra 命令及参数

1. Segment(A, C) → a
2. Segment(C, B) → b
3. Segment(B, A) → c
4. Rotate(C, Angle[B, A, D], B) → C'
5. Segment(B, C') → g
6. Rotate(B, -Angle[D, B, A], C) → B'
7. Segment(C, B') → f
8. Intersect(g, f) → E
9. Rotate(A, Angle[B, A, D], C) → A'
10. Segment(C, A') → j
11. Rotate(C, -Angle[D, B, A], A) → C'_1
12. Segment(A, C'_1) → k
13. Intersect(j, k) → F
14. Segment(D, F) → n
15. Segment(D, E) → p
16. Segment(F, E) → q
17. Angle(C, A, B) → α
18. Angle(B, C, A) → β
19. Angle(A, B, C) → γ
20. Angle(F, D, E) → δ
21. Angle(D, E, F) → ε
22. Angle(E, F, D) → ζ
23. Midpoint(q) → G
24. Midpoint(p) → H
25. Midpoint(n) → I
26. Segment(I, E) → d
27. Segment(D, G) → e
28. Intersect(d, e) → J
29. Midpoint(b) → K
30. Midpoint(a) → L
31. Segment(L, B) → h
32. Segment(A, K) → i