Four Points in Normal Form

GeoGebra Commands & Parameters

1. LineBisector(z_{1}, z_{2}) → l_1
2. LineBisector(z_{3}, z_{2}) → a_3
3. Circle(z_{3}, z_{2}, z_{1}) → t_3
4. Tangent(z_{3}, t_3) → f_4,
5. Circle(z_{2}, z_{3}, z_{1}) → c_{123}
6. Tangent(z_{1}, c_{123}) → m_1,
7. Circle(z_{3}, z_{2}, z_{4}) → c_4
8. Tangent(z_{3}, c_4) → b_3,
9. AngularBisector(b_3, f_4) → g_4, h_4
10. Intersect(a_3, g_4) → H_1
11. Circle(H_1, z_{2}) → e_4
12. LineBisector(z_{4}, z_{1}) → l_3
13. LineBisector(z_{3}, z_{4}) → a_1
14. Circle(z_{3}, z_{4}, z_{1}) → c_{341}
15. Tangent(z_{3}, c_{341}) → f_2,
16. Circle(z_{3}, z_{4}, z_{2}) → c_{342}
17. Tangent(z_{3}, c_{342}) → b_1,
18. AngularBisector(b_1, f_2) → g_2, p_2
19. Intersect(a_1, p_2) → O
20. Circle(O, z_{3}) → cw_{34}
21. Circle(z_{1}, z_{3}, z_{4}) → c_{1}
22. Tangent(z_{1}, c_{1}) → n_3,
23. Circle(z_{1}, z_{4}, z_{2}) → c_{3}
24. Tangent(z_{1}, c_{3}) → m_3,
25. AngularBisector(n_3, m_3) → p_3, q_3
26. Intersect(p_3, l_3) → F_1
27. Circle(F_1, z_{4}) → s_3
28. Intersect(s_3, e_4) → z_o, z_{∞}, ,
29. Circle(z_{1}, z_{2}, z_{4}) → c_{124}
30. Tangent(z_{1}, c_{124}) → n_1,
31. AngularBisector(m_1, n_1) → q_1, r_1
32. Intersect(l_1, r_1) → L
33. Circle(L, z_{1}) → s_1
34. Intersect(s_1, cw_{34}) → z_e, z'_e, ,
35. Line(z_{1}, z_{2}) → gf
36. Tangent(z_{3}, c_{123}) → g,
37. Intersect(gf, g) → A
38. Circle(z_{2}, z_{1}, z_{3}) → c_{132}
39. Line(z_{3}, z_{4}) → h
40. Tangent(z_{1}, c_{132}) → gi,
41. Intersect(h, gi) → B
42. Circle(B, z_{1}) → k
43. Tangent(z_{4}, c_{124}) → n,
44. Intersect(gf, n) → D
45. Circle(D, z_{4}) → c4o_{12}
46. Tangent(z_{2}, c_{123}) → b,
47. Tangent(z_{1}, c_{123}) → d,
48. Intersect(d, b) → m_o
49. Circle(m_o, z_{1}) → c_{o123}
50. If(Intersect[c_{o123}, c_{132}, 1] ≟ z_{1}, Intersect[c_{o123}, c_{132}, 2], Intersect[c_{o123}, c_{132}, 1]) → zo_4
51. Intersect(h, gf) → E
52. Circle(A, z_{3}) → c3o_{12}
53. Circle(z_{3}, z_{1}, z_{4}) → c_{134}
54. If(Intersect[c_{134}, c3o_{12}, 1] ≟ z_{3}, Intersect[c_{134}, c3o_{12}, 2], Intersect[c_{134}, c3o_{12}, 1]) → zso_4
55. Intersect(c_{123}, c4o_{12}, 2) → z''_4
56. Intersect(c_{123}, c4o_{12}, 1) → z'''_4
57. If(abs(z''_4 - z_{4}) < abs(z'''_4 - z_{4}), z''_4, z'''_4) → zConz_4
58. Tangent(z_{1}, c_{3}) → l,
59. LineBisector(z_{3}, z_{1}) → q
60. AngularBisector(gi, l) → s, c
61. Intersect(q, c) → H
62. Intersect(q, s) → I
63. LineBisector(z_{3}, z_{4}) → f_1
64. Tangent(z_{4}, c_{134}) → h_1,
65. Intersect(l_1, q_1) → M
66. Circle(M, z_{1}) → t_1
67. Tangent(z_{1}, s_1) → i_2,
68. Tangent(z_{1}, t_1) → j_2,
69. LineBisector(z_{1}, z_{2}) → k_2
70. AngularBisector(j_2, i_2) → l_2, m_2
71. Intersect(j_2, k_2) → U
72. Intersect(k_2, m_2) → V
73. Intersect(k_2, l_2) → W
74. LineBisector(z_{3}, z_{2}) → h_2
75. LineBisector(z_{4}, z_{2}) → n_2
76. Intersect(a_1, g_2) → N
77. Circle(N, z_{3}) → cw'_{34}
78. LineBisector(z'_e, z_e) → r_2
79. Tangent(z_e, cw_{34}) → s_2,
80. Tangent(z_e, s_1) → t_2,
81. AngularBisector(s_2, t_2) → a_2, b_2
82. Intersect(r_2, b_2) → R
83. Circle(R, z_e) → w'_{12}
84. Intersect(r_2, a_2) → S
85. Circle(S, z_e) → w_{12}
86. LineBisector(z_{1}, z_{3}) → g_1
87. Tangent(z_{1}, c_{134}) → i_1,
88. Tangent(z_{1}, c_{132}) → j_1,
89. AngularBisector(i_1, j_1) → k_1, p_1
90. Intersect(g_1, p_1) → J
91. Circle(J, z_{1}) → cw_{13}
92. Intersect(g_1, k_1) → K
93. Circle(K, z_{1}) → cw'_{13}
94. Circle(z_{4}, z_{2}, z_{3}) → c_{243}
95. Circle(z_{4}, z_{2}, z_{1}) → c_{241}
96. LineBisector(z_{4}, z_{2}) → q_2
97. Tangent(z_{4}, c_{241}) → c_2,
98. Tangent(z_{4}, c_{243}) → d_2,
99. AngularBisector(d_2, c_2) → e_2, f_3
100. Intersect(q_2, f_3) → T
101. Circle(T, z_{2}) → cw_{24}
102. Intersect(q_2, e_2) → Z
103. Circle(Z, z_{2}) → cw'_{24}
104. Intersect(cw_{24}, cw_{13}) → z_i, z'_i, ,
105. LineBisector(z_i, z'_i) → g_3
106. Tangent(z'_i, cw_{24}) → h_3,
107. Tangent(z'_i, cw_{13}) → i_3,
108. AngularBisector(i_3, h_3) → j_3, k_3
109. Intersect(g_3, k_3) → C_1
110. Circle(C_1, z_i) → d_3
111. Intersect(g_3, j_3) → D_1
112. Circle(D_1, z_i) → e_3
113. Intersect(q_3, l_3) → E_1
114. Circle(E_1, z_{1}) → r_3
115. Intersect(h_4, a_3) → G_1
116. Circle(G_1, z_{2}) → d_4
117. LineBisector(z_o, z_{∞}) → d_1
118. Tangent(z_o, e_4) → e_1,
119. Tangent(z_o, s_3) → i_4,
120. AngularBisector(i_4, e_1) → j_4, k_4
121. Intersect(d_1, k_4) → K_1
122. Circle(K_1, z_o) → p_4
123. Intersect(d_1, j_4) → L_1
124. Circle(L_1, z_o) → q_4
125. Circle(o', e) → c_E
126. Line(o', e) → g_x
127. Line(o', i) → g_y