几何均值高定理

GeoGebra 命令及参数

1. Point(f) → A
2. Line(A, B) → g
3. OrthogonalLine(B, g) → h_1
4. Intersect(f, h_1) → C
5. OrthogonalLine(B, f) → i
6. Intersect(f, i) → D
7. Segment(A, C) → j
8. Segment(C, B) → k
9. Segment(B, A) → l
10. Segment(D, B) → h
11. Angle(C, D, B) → α
12. Angle(A, B, C) → β
13. Segment(A, D) → a
14. Segment(D, C) → b
15. Polygon(A, B, D) → t1, d, a_1, b_1
16. Dilate(D, If[0 ≤ c < 1, 1 - c, 0], E) → E'
17. Vector(D, E') → v
18. Translate(A, v) → A'
19. Translate(B, v) → B'
20. Translate(D, v) → D'
21. Polygon(A', B', D') → t1', d', a', b'
22. Rotate(A', If[1 ≤ c < 2, ((1 - c) * π / 2), (3 * π / 2)], E) → A''
23. Rotate(B', If[1 ≤ c < 2, ((1 - c) * π / 2), (3 * π / 2)], E) → B''
24. Rotate(D', If[1 ≤ c < 2, ((1 - c) * π / 2), (3 * π / 2)], E) → D''
25. Polygon(A'', B'', D'') → t1'', d'', a'', b''
26. Polygon(D, C, B) → t2, b_2, d_1, c_1
27. Dilate(D, If[2 ≤ c < 3, 3 - c, 0], F) → F'
28. Vector(D, F') → u
29. Translate(D, u) → D'_1
30. Translate(C, u) → C'
31. Translate(B, u) → B'_1
32. Polygon(D'_1, C', B'_1) → t2', b'_1, d'_1, c'
33. Angle(B', D', A') → γ
34. Angle(B'', D'', A'') → δ
35. Angle(C', D'_1, B'_1) → ε