Triangle Area Exploration

GeoGebra Commands & Parameters

1. Rotate(A, α, B) → A'
2. Angle(A, B, A') → γ
3. Ray(B, A') → f
4. Rotate(B, (-β), A) → B'
5. Angle(B', A, B) → δ
6. Ray(A, B') → g
7. Segment(B, A) → h
8. Intersect(f, g) → C
9. Segment(B, C) → i
10. Segment(A, C) → j
11. Midpoint(i) → D
12. Midpoint(j) → E
13. Line(B, A) → l
14. OrthogonalLine(C, l) → m
15. Intersect(l, m) → F
16. Segment(C, F) → n
17. Polygon(D, E, C) → poly1, c, d, e
18. Midpoint(n) → G
19. Line(C, l) → p
20. Polygon(B, D, E, A) → poly2, b, d_1, e_1, a
21. Segment(D, C) → q
22. Segment(B, A) → r
23. Point(p) → H
24. OrthogonalLine(H, p) → t
25. Intersect(l, t) → I
26. Segment(H, I) → s
27. Circle(I, 3) → c_1
28. Circle(H, 3) → f_1
29. Intersect(f_1, p, 1) → J
30. Intersect(f_1, p, 2) → K
31. Intersect(c_1, l, 2) → L
32. Intersect(c_1, s, 1) → M
33. Intersect(c_1, l, 1) → N
34. Angle(J, H, I) → ε
35. Angle(M, I, N) → ζ
36. Dilate(H, If[0 < k ≤ 1, 1 - k, 0], I) → H'
37. Segment(H, H') → g_1
38. Angle(C, F, B) → η
39. Dilate(C, If[1 < k ≤ 2, 2 - k, 0], G) → C'
40. Segment(C, C') → h_1
41. Dilate(G, If[2 < k ≤ 3, 3 - k, 0], F) → G'
42. Segment(G, G') → i_1
43. Rotate(C, If[3 < k ≤ 4, ((-(k - 3)) * π), (-π)], G) → C'_1
44. Rotate(C', If[3 < k ≤ 4, ((-(k - 3)) * π), (-π)], G) → C''
45. Segment(C'_1, C'') → j_1
46. Dilate(G, If[4 < k ≤ 5, 5 - k, 0], D) → G'_1
47. Dilate(G, If[4 < k ≤ 5, 5 - k, 0], E) → G'_2
48. Segment(G, G'_1) → k_1
49. Segment(G, G'_2) → l_1
50. Segment(B, F) → m_1
51. Segment(B, D) → n_1
52. Segment(D, G) → p_1
53. Segment(D, C) → q_1
54. Min({m_1, n_1, p_1, q_1}) → o
55. Circle(B, (0.6 * o)) → r_1
56. Intersect(r_1, l) → O, P
57. Segment(B, C) → s_1
58. Intersect(r_1, s_1, 1) → Q
59. CircleSector(B, P, Q) → t_1
60. Rotate(D, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → D'
61. Rotate(E, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → E'
62. Rotate(C, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → C'_2
63. Polygon(D', E', C'_2) → poly1', c'_2, d', e'
64. Segment(D, C) → a_1
65. Segment(D, B) → b_1
66. Segment(C, E) → f_2
67. Segment(E, A) → g_2
68. Segment(E, C'_2) → h_2
69. Segment(C'_2, D') → i_2
70. Segment(D', E) → j_2
71. Dilate(D, If[7 < k ≤ 8, 8 - k, 0], C) → D'_1
72. Segment(D, D'_1) → k_2
73. Dilate(B, If[8 < k ≤ 9, 9 - k, 0], D) → B'_1
74. Vector(B, B'_1) → u
75. Translate(t_1, u) → c_2
76. Dilate(B, If[9 < k ≤ 10, 10 - k, 0], A) → B'_2
77. Vector(B, B'_2) → v
78. Translate(t_1, v) → d_2
79. Circle(A, Radius[r_1]) → e_2
80. Intersect(e_2, l, 1) → R
81. Intersect(e_2, g_2, 1) → S
82. Segment(B, A) → l_2
83. Segment(A, C) → m_2
84. Min({l_2, m_2}) → w
85. Circle(A, (0.25 * w)) → p_2
86. Intersect(g_2, m_2) → T
87. Intersect(g_2, m_2) → U
88. Intersect(p_2, m_2) → V,
89. Intersect(p_2, l_2) → W,
90. CircleSector(A, V, W) → q_2
91. Segment(B, A) → n_2