Triangle Area by Åsmund Børsum

GeoGebra Commands & Parameters

1. Circle(A, Height) → c
2. Circle(A, Base) → d
3. Point(d) → B
4. Segment(A, B) → e
5. Line(A, B) → f
6. OrthogonalLine(A, f) → g
7. Intersect(c, g, 1) → C
8. Tangent(C, c) → h, a
9. Polygon(A, B, D) → P, d_1, a_1, b_1
10. OrthogonalLine(D, f) → i
11. Intersect(f, i) → E
12. Segment(E, D) → j
13. Segment(E, B) → k
14. Midpoint(D, B) → F
15. Midpoint(D, A) → G
16. Point(a_1) → H
17. Circle(B, H) → p
18. Intersect(p, d_1, 1) → I
19. OrthogonalLine(H, a_1) → l
20. OrthogonalLine(I, d_1) → m
21. Intersect(l, m) → J
22. If(x(D) ≟ x(B), G) → K
23. If(x(D) ≟ x(B), J) → L
24. Segment(L, H) → n
25. Segment(L, I) → q
26. Rotate(A, Hint, K) → A'
27. Rotate(B, Hint, K) → B'
28. Rotate(D, Hint, K) → D'
29. Polygon(A', B', D') → P', d', a', b'
30. If(x(D) ≟ x(A), F) → M
31. Point(b_1) → N
32. Circle(A, N) → r
33. Intersect(r, d_1, 1) → O
34. OrthogonalLine(N, b_1) → s
35. OrthogonalLine(O, d_1) → t
36. Intersect(s, t) → Q
37. If(x(D) ≟ x(A), Q) → R
38. Segment(N, R) → c_1
39. Segment(R, O) → e_1
40. Rotate(A, (-Hint), M) → A'_1
41. Rotate(B, (-Hint), M) → B'_1
42. Rotate(D, (-Hint), M) → D'_1
43. Polygon(A'_1, B'_1, D'_1) → P'_1, d'_1, a'_1, b'_1
44. If(x(D) > x(B), G) → S
45. Rotate(A, Hint, S) → A'_2
46. Rotate(B, Hint, S) → B'_2
47. Rotate(D, Hint, S) → D'_2
48. Polygon(A'_2, B'_2, D'_2) → P'_2, d'_2, a'_2, b'_2
49. If(x(D) < x(A), F) → T
50. Rotate(A, (-Hint), T) → A'_3
51. Rotate(B, (-Hint), T) → B'_3
52. Rotate(D, (-Hint), T) → D'_3
53. Polygon(A'_3, B'_3, D'_3) → P'_3, d'_3, a'_3, b'_3
54. If((x(D) > x(A)) ∧ (x(D) < x(B)), F) → U
55. Rotate(A, (-Hint), U) → A'_4
56. Rotate(B, (-Hint), U) → B'_4
57. Rotate(D, (-Hint), U) → D'_4
58. Polygon(A'_4, B'_4, D'_4) → P'_4, d'_4, a'_4, b'_4
59. Midpoint(D, E) → V
60. Midpoint(A, B) → W
61. Polygon(Z_1, A, D) → Mangekant1, d_2, z_1, a_2
62. Midpoint(a_2) → Z
63. Rotate(D, Hint, Z) → A_2
64. Rotate(A, Hint, Z) → A_3
65. Rotate(Z_1, Hint, Z) → A_1
66. Polygon(A_2, A_3, A_1) → Mangekant2, a_3, a_4, a_5