两数平方差的两倍等于一加两数和的平方的证明

GeoGebra 命令及参数

1. Line(A, xAxis) → f
2. Point(Circle[A, a]) → B
3. Segment(A, B) → g
4. OrthogonalLine(A, f) → h
5. Circle(A, B) → c
6. Intersect(c, h, 2) → C
7. OrthogonalLine(B, f) → i
8. OrthogonalLine(C, h) → j
9. Intersect(i, j) → D
10. Point(Circle[B, a]) → E
11. Segment(B, E) → k
12. OrthogonalLine(E, f) → l
13. Intersect(j, l) → F
14. Point(Circle[C, a + 1]) → G
15. Segment(C, G) → m
16. Circle(C, G) → d
17. Intersect(d, h, 2) → H
18. OrthogonalLine(G, j) → n
19. OrthogonalLine(H, n) → p
20. Point(Circle[G, a + 1]) → I
21. Segment(G, I) → q
22. OrthogonalLine(I, j) → r
23. Intersect(p, r) → J
24. Intersect(n, p) → K
25. Segment(A, B) → s
26. Segment(B, D) → t
27. Segment(D, C) → b
28. Segment(C, A) → e
29. Segment(B, E) → f_1
30. Segment(E, F) → g_1
31. Segment(F, D) → h_1
32. Segment(C, H) → i_1
33. Segment(H, K) → j_1
34. Segment(K, G) → k_1
35. Segment(K, J) → l_1
36. Segment(J, I) → m_1
37. Circle(C, D) → c_1
38. Intersect(c_1, i_1) → L,
39. OrthogonalLine(L, i_1) → n_1
40. Intersect(i, n_1) → M
41. Intersect(l, n_1) → N
42. Segment(D, M) → p_1
43. Segment(M, L) → q_1
44. Segment(M, N) → r_1
45. Segment(N, F) → s_1
46. Intersect(n_1, m_1) → O
47. Intersect(l, l_1) → P
48. Segment(N, P) → t_1
49. Segment(N, O) → a_1
50. Polygon(A, B, D, C) → poly1, a_2, b_1, d_1, c_2
51. Polygon(B, E, F, D) → poly2, b_2, e_1, f_2, d_2
52. Polygon(F, N, M, D) → poly3, f_3, n_2, m_2, d_3
53. Polygon(D, C, L, M) → poly4, d_4, c_3, l_2, m_3
54. Segment(L, H) → g_2
55. Polygon(F, I, O, N) → poly5, f_4, i_2, o, n_3
56. Polygon(N, L, H, P) → poly6, n_4, l_3, h_2, p_2
57. Polygon(N, P, J, O) → poly7, n_5, p_3, j_2, o_1
58. Segment(D, G) → k_2