Sum of Distances from a Point to Sides of an Equilateral Triangle

GeoGebra Commands & Parameters

1. Polygon(A, B, 3) → poly1, f, g, h, C
2. PointIn(poly1) → P
3. OrthogonalLine(P, g) → i
4. OrthogonalLine(P, f) → j
5. OrthogonalLine(P, h) → k
6. Intersect(j, f) → E
7. Intersect(k, h) → F
8. Intersect(i, g) → G
9. Segment(C, A) → l
10. Segment(A, B) → m
11. Segment(B, C) → n
12. Segment(F, P) → p
13. Segment(P, G) → q
14. Segment(P, E) → r
15. Rotate(G, 30°, P) → G'
16. Angle(G, P, G') → α
17. Rotate(G, -30°, P) → G'_{1}
18. Angle(G'_{1}, P, G) → β
19. Ray(P, G') → s
20. Ray(P, G'_{1}) → t
21. Intersect(n, s) → H
22. Intersect(n, t) → I
23. Rotate(F, 30°, P) → F'
24. Angle(F, P, F') → γ
25. Rotate(F, -30°, P) → F'_{1}
26. Angle(F'_{1}, P, F) → δ
27. Ray(P, F'_{1}) → a
28. Ray(P, F') → b
29. Intersect(l, a) → J
30. Intersect(l, b) → K
31. Rotate(E, 30°, P) → E'
32. Angle(E, P, E') → ε
33. Rotate(E, -30°, P) → E'_{1}
34. Angle(E'_{1}, P, E) → ζ
35. Ray(P, E'_{1}) → c
36. Ray(P, E') → d
37. Intersect(m, c) → L
38. Intersect(m, d) → M
39. Polygon(J, P, K) → t1, k_1, j_1, d_1
40. Polygon(P, L, M) → t2, m_1, d_2, l_1
41. Polygon(P, H, I) → t3, i_1, d_3, h_1
42. Centroid(t3) → N
43. Rotate(P, (-η), N) → D'
44. Rotate(H, (-η), N) → H'
45. Rotate(I, (-η), N) → I'
46. Polygon(D', H', I') → t3', i', d', h'
47. Rotate(P, (-η), N) → D'_{1}
48. Rotate(G, (-η), N) → G'_{2}
49. Segment(D'_{1}, G'_{2}) → q'
50. Line(C, P) → e
51. Centroid(t1) → O
52. Rotate(J, (-θ), O) → J'
53. Rotate(P, (-θ), O) → D'_{2}
54. Rotate(K, (-θ), O) → K'
55. Polygon(J', D'_{2}, K') → t1', k', j', d'_{2}
56. Rotate(F, (-θ), O) → F'_{2}
57. Rotate(P, (-θ), O) → D'_{3}
58. Segment(F'_{2}, D'_{3}) → p'
59. Circle(J, o) → c_1
60. Distance(J, C) → dJC
61. Intersect(c_1, l, 1) → P_{1}
62. Vector(J, P_{1}) → u
63. Translate(J', u) → J''
64. Translate(D'_{2}, u) → Q
65. Translate(K', u) → K''
66. Polygon(J'', Q, K'') → t1'', k'', j'', q_1
67. Translate(F'_{2}, u) → R
68. Translate(D'_{3}, u) → S
69. Segment(R, S) → p''
70. Segment(V, W) → g_1
71. Midpoint(V, W) → A_1
72. OrthogonalLine(A_1, g_1) → f_1
73. OrthogonalLine(C, f_1) → n_1
74. Intersect(f_1, n_1) → T
75. OrthogonalLine(A_1, g_1) → p_1
76. OrthogonalLine(V, g_1) → r_1
77. OrthogonalLine(W, g_1) → s_1
78. Intersect(r_1, n_1) → U
79. Intersect(n_1, s_1) → Z
80. OrthogonalLine(H, p_1) → t_1
81. Intersect(f_1, p_1) → C_1
82. Intersect(f_1, p_1) → D_1
83. Intersect(t_1, f_1) → E_1
84. Distance(H, E_1) → dHE1
85. OrthogonalLine(P, p_1) → a_1
86. Intersect(f_1, p_1) → I_1
87. Intersect(f_1, p_1) → J_1
88. Intersect(f_1, p_1) → K_1
89. Intersect(f_1, p_1) → L_1
90. Intersect(a_1, f_1) → M_1
91. Distance(P, M_1) → dDM1
92. Circle(P, (v * dDM1 / 6)) → e_2
93. Intersect(e_2, a_1, 1) → N_1
94. Vector(P, N_1) → v_1
95. Translate(P, v_1) → D'_{4}
96. Translate(E, v_1) → E'_{2}
97. Segment(D'_{4}, E'_{2}) → r'
98. Segment(U, Z) → b_1
99. Segment(T, A_1) → f_2
100. Segment(C, T) → g_2
101. Segment(B, A_1) → h_2
102. Segment(H, E_1) → i_2
103. Segment(P, M_1) → j_2
104. Circle(C, v) → c_2
105. Intersect(c_2, n_1, 1) → B_1
106. Vector(C, B_1) → w
107. Translate(R, w) → R'
108. Translate(S, w) → S'
109. Segment(R', S') → p'''
110. Circle(H, (v * dHE1 / 6)) → k_2
111. Intersect(k_2, t_1, 1) → F_1
112. Vector(H, F_1) → u_1
113. Translate(D'_{1}, u_1) → G_1
114. Translate(G'_{2}, u_1) → H_1
115. Segment(G_1, H_1) → q''
116. Point(g) → O_1
117. Circle(B, A) → p_2
118. Circle(A, B) → q_2
119. Intersect(p_2, q_2) → D, Q_1, ,