Dynamic Excircle Relationship in Triangles

GeoGebra Commands & Parameters

1. Rotate(B, (a * π / 180), A) → B'
2. Ray(A, B') → g
3. Point(g) → C
4. Segment(A, C) → j
5. Circle(C, 4) → c
6. Intersect(c, g, 2) → E
7. Ray(A, B) → f
8. Point(f) → D
9. Segment(C, D) → h
10. Angle(D, C, E) → γ
11. Rotate(D, γ / 2, C) → D'
12. Ray(C, D') → m
13. Segment(A, D) → i
14. Min({i, j, h}) → b
15. Circle(D, (0.2 * b)) → d
16. Intersect(d, f, 2) → F
17. Ray(D, F) → k
18. Angle(F, D, C) → β
19. Rotate(F, β / 2, D) → F'
20. Ray(D, F') → n
21. Intersect(m, n) → J
22. Line(J, h) → l_2
23. Intersect(k, l_2) → P
24. Ray(C, E) → l
25. Intersect(l, l_2) → O
26. Angle(B, A, B') → α
27. Circle(C, (0.2 * b)) → e
28. Circle(D, (0.15 * b)) → p
29. Angle(F, D, F') → δ
30. Angle(D, C, D') → ε
31. Intersect(e, m, 1) → G
32. Intersect(e, h, 1) → H
33. Intersect(p, h, 1) → I
34. CircleSector(C, H, G) → q
35. CircleSector(D, F, F') → r
36. OrthogonalLine(J, k) → s
37. OrthogonalLine(J, l) → t
38. Intersect(s, k) → K
39. Intersect(t, l) → L
40. Circle(J, K) → c_1
41. Segment(L, K) → f_1
42. Midpoint(f_1) → M
43. OrthogonalLine(M, f_1) → g_1
44. Intersect(c_1, g_1, 2) → N
45. Segment(N, C) → h_1
46. Segment(N, D) → i_1
47. Polygon(A, D, C) → poly1, c_2, a_1, d_2
48. Angle(J, K, D) → ζ
49. Angle(C, L, J) → η
50. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
51. Segment(A, A') → k_1
52. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'_1
53. Segment(A, A'_1) → l_1
54. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], J) → C'
55. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], J) → D'_1
56. Segment(C, C') → m_1
57. Segment(D, D'_1) → n_1
58. Rotate(r, If[2.5 < o ≤ 3.5, ((o - 2.5) * δ), δ], D) → r'
59. Rotate(q, If[3.5 < o ≤ 4.5, ((o - 3.5) * ε), ε], C) → q'
60. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], L) → J'
61. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], K) → J'_1
62. Segment(J, J'_1) → p_1
63. Segment(J, J') → q_1
64. Angle(L, J, K) → θ
65. Rotate(L, If[6 < o ≤ 7, ((o - 6) * θ), θ], J) → L'
66. CircleArc(J, L, L') → e_1
67. Rotate(K, If[7 < o ≤ 8, ((o - 7) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → K'
68. CircleArc(J, K, K') → r_1
69. Rotate(N, If[8 < o ≤ 9, ((o - 8) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → N'
70. CircleArc(J, N, N') → s_1
71. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], D) → N'_1
72. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], C) → N'_2
73. Min(c_2, d_2) → w
74. Circle(A, (0.15 * w)) → e_2
75. Segment(A, C) → m_2
76. Intersect(e_2, m_2) → S,
77. Segment(A, D) → n_2
78. Intersect(e_2, n_2) → T,
79. Min({h, k_1, l_1}) → b_1
80. Intersect(d, h, 1) → U
81. Intersect(e, h) → W,
82. Angle(A, C, D) → λ
83. Angle(C, D, A) → κ
84. Rotate(A, λ / 2, C) → A'_2
85. Angle(A, C, A'_2) → ι
86. Ray(C, A'_2) → t_1
87. Rotate(C, κ / 2, D) → C'_1
88. Angle(C, D, C'_1) → μ_1
89. Ray(D, C'_1) → f_2
90. Intersect(d, f_2) → A_1,
91. CircleSector(D, U, A_1) → r_2
92. Intersect(t_1, f_2) → Z
93. OrthogonalLine(Z, k_1) → s_2
94. OrthogonalLine(Z, l_1) → t_2
95. Intersect(s_2, k_1) → B_1
96. Intersect(t_2, l_1) → C_1
97. Intersect(k_1, t_1) → D_1
98. Circle(A, (0.2 * b)) → q_2
99. Angle(D, A, C) → μ
100. Rotate(D, μ / 2, A) → D'_2
101. Angle(D, A, D'_2) → ν
102. Ray(A, D'_2) → a_2
103. Intersect(q_2, a_2) → V,
104. Intersect(q_2, k_1) → E_1,
105. CircleSector(A, E_1, V) → p_2
106. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], Z) → D'_3
107. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], Z) → A'_3
108. Segment(A, A'_3) → b_2
109. Segment(D, D'_3) → f_3
110. Rotate(r_2, If[2.5 < o ≤ 3.5, ((o - 2.5) * κ / 2), κ / 2], D) → c_3
111. Rotate(p_2, If[3.5 < o ≤ 4.5, ((o - 3.5) * μ / 2), μ / 2], A) → d_3
112. Dilate(Z, If[5 < o ≤ 6, 6 - o, 0], C_1) → Z'
113. Dilate(Z, If[5 < o ≤ 6, 6 - o, 0], B_1) → Z'_1
114. Segment(Z, Z') → g_3
115. Segment(Z, Z'_1) → h_3
116. Angle(Z, B_1, A) → ξ
117. Angle(A, C_1, Z) → ο
118. Circle(Z, Z') → e_3
119. Rotate(C_1, If[6 < o ≤ 9, (((o - 6) * 2) * π / 3), (2 * π)], Z) → F_1
120. Segment(C, D_1) → i_3
121. Intersect(e, i_3) → G_1,
122. Dilate(C, If[9.5 < o ≤ 10.5, 10.5 - o, 0], Z) → C'_2
123. Dilate(J, If[9.5 < o ≤ 10.5, 10.5 - o, 0], Z) → J'_2
124. Polygon(A, Z, C) → poly2, c_4, a_3, z_1
125. Polygon(A, D, J) → poly3, j_2, a_4, d_4
126. CircleArc(Z, Z', F_1) → k_3
127. Dilate(C, If[11 < o ≤ 12, 12 - o, 0], J) → C'_3
128. Vector(C, C'_3) → u_1
129. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], O) → C'_4
130. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], P) → D'_4
131. Segment(C, C'_4) → j_1
132. Segment(D, D'_4) → d_1
133. Line(C, O) → g_2
134. Line(D, P) → h_2
135. Circle(P, 5) → k_2
136. Circle(O, 5) → p_3
137. Intersect(k_2, h_2) → Q, R
138. Intersect(p_3, g_2) → H_1, I_1
139. Ray(P, R) → i_2
140. Ray(O, I_1) → j_3
141. Line(O, J) → l_3
142. Circle(O, C) → r_3
143. Dilate(J, If[11 < o ≤ 12, 12 - o, 0], O) → J'_3
144. Dilate(J, If[11 < o ≤ 12, 12 - o, 0], P) → J'_4
145. Segment(J, J'_3) → s_3
146. Segment(J, J'_4) → t_3
147. Dilate(D, If[12 < o ≤ 13, 13 - o, 0], P) → D'_5
148. Vector(D, D'_5) → w_1
149. Translate(c_3, w_1) → e_4
150. Translate(D, w_1) → D'_6
151. Translate(D'_3, w_1) → K_1
152. Segment(D'_6, K_1) → b_3
153. Angle(C, D, Z) → ρ
154. Rotate(e_4, If[13.5 < o ≤ 14.5, ((-(o - 13.5)) * ρ), (-ρ)], P) → q_3
155. Angle(A, C, D) → σ
156. Rotate(C, If[15 < o ≤ 16, ((o - 15) * σ), σ], O) → C'_5
157. Rotate(C'_4, If[15 < o ≤ 16, ((o - 15) * σ), σ], O) → J_1
158. Segment(C'_5, J_1) → m_3
159. Rotate(D, If[16 < o ≤ 17, (((-(o - 16)) * 2) * ρ), (-2 * ρ)], P) → D'_7
160. Rotate(D'_4, If[16 < o ≤ 17, (((-(o - 16)) * 2) * ρ), (-2 * ρ)], P) → L_1
161. Segment(D'_7, L_1) → n_3