“坐在栅栏上”：绝对值不等式的几何求解

GeoGebra 命令及参数

1. Ray(A, B) → f
2. Ray(A, C) → g
3. Point(f) → E
4. Mirror(E, A) → E'
5. Vector(A, E) → u
6. Vector(A, E') → v
7. Distance(A, E) → distanceAE
8. Distance(A, E') → distanceAE'
9. Ray(F, H) → h
10. Ray(D, G) → l
11. Segment(D, F) → m
12. Circle(A, 1) → c
13. Circle(E', 1) → d
14. Circle(E, 1) → e
15. Circle(D, 4) → c_1
16. Circle(F, 4) → d_1
17. Intersect(c_1, t, 1) → L
18. Intersect(d_1, t, 1) → M
19. Segment(D, L) → f_1
20. Segment(F, M) → g_1
21. Polygon(O, N, 4) → poly1, h_1, i_1, j_1, k_1, R, S
22. Polygon(Q, P, 4) → poly2, l_1, m_1, n_1, p_1, T, U
23. Distance(S, R) → distanceSR
24. Distance(U, T) → distanceUT
25. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], E) → A'
26. Segment(A, A') → q_1
27. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], E') → A'_1
28. Segment(A, A'_1) → r_1
29. Dilate(F, If[1 < b ≤ 2, 2 - b, 0], M) → F'
30. Dilate(D, If[1 < b ≤ 2, 2 - b, 0], L) → D'
31. Segment(F, F') → p
32. Segment(D, D') → q
33. Translate(poly1, (-1.5, 0)) → poly1'
34. Translate(poly2, (1.5, 0)) → poly2'
35. Distance(U, T) → e_1
36. Distance(S, R) → o_1