Animation Demonstrating Circumcircle and Incircle

GeoGebra Commands & Parameters

1. Rotate(A, a°, B) → A'
2. Angle(A, B, A') → α
3. Segment(B, A) → f
4. Ray(B, A') → g
5. Point(g) → C
6. Segment(A, C) → h
7. Segment(B, C) → i
8. Rotate(A, α / 2, B) → A'_1
9. Angle(A, B, A'_1) → β
10. Ray(B, A'_1) → j
11. Angle(C, A, B) → γ
12. Rotate(C, γ / 2, A) → C'
13. Angle(C, A, C') → δ
14. Ray(A, C') → k
15. Intersect(k, j) → D
16. LineBisector(h) → l
17. LineBisector(i) → m
18. Intersect(l, m) → E
19. OrthogonalLine(D, i) → n
20. OrthogonalLine(D, h) → p
21. Intersect(n, i) → F
22. Intersect(p, h) → G
23. Angle(D, G, A) → ε
24. Angle(D, F, C) → ζ
25. Min(f, i) → b
26. Circle(A, (0.2 * b)) → c
27. Circle(B, (0.2 * b)) → d
28. Intersect(c, h, 1) → H
29. Intersect(c, k, 1) → I
30. Intersect(d, f, 1) → J
31. Intersect(d, j, 1) → K
32. CircleSector(A, H, I) → e
33. CircleSector(B, J, K) → q
34. Intersect(i, k) → L
35. Intersect(h, j) → M
36. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], L) → A'_2
37. Segment(A, A'_2) → r
38. Dilate(B, If[1 < o ≤ 2, 2 - o, 0], D) → B'
39. Segment(B, B') → s
40. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], M) → D'
41. Segment(D, D') → t
42. Rotate(e, If[3 < o ≤ 4, ((o - 3) * γ / 2), γ / 2], A) → e'
43. Rotate(q, If[4 < o ≤ 5, ((o - 4) * α / 2), α / 2], B) → q'
44. Circle(D, F) → c_1
45. Rotate(F, If[5 < o ≤ 7, ((o - 5) * π), π], D) → F'
46. CircleArc(D, F, F') → d_1
47. Dilate(E, If[8 < o ≤ 9, 9 - o, 0], C) → E'
48. Segment(E, E') → f_1
49. Circle(E, C) → e_1
50. Rotate(C, If[9 < o ≤ 11, ((o - 9) * π), π], E) → C'_1
51. CircleArc(E, C, C'_1) → g_1
52. Min({y(E), y(A), y(B), y(C)}) → u
53. OrthogonalLine(E, h_1) → j_1
54. Intersect(h_1, j_1) → N
55. Intersect(i_1, j_1) → O
56. OrthogonalLine(E, h) → k_1
57. OrthogonalLine(E, i) → l_1
58. OrthogonalLine(E, f) → m_1
59. Intersect(l_1, i) → P
60. Intersect(k_1, h) → Q
61. Intersect(m_1, f) → R
62. Dilate(E, If[11 < o ≤ 12, 12 - o, 0], P) → E'_1
63. Dilate(E, If[11 < o ≤ 12, 12 - o, 0], Q) → E'_2
64. Dilate(E, If[11 < o ≤ 12, 12 - o, 0], R) → E'_3
65. Segment(E, E'_1) → n_1
66. Segment(E, E'_2) → p_1
67. Segment(E, E'_3) → q_1
68. Angle(E, Q, C) → η
69. Angle(E, P, C) → θ
70. Angle(E, R, B) → ι
71. Dilate(E, If[12 < o ≤ 13, 13 - o, 0], N) → E'_4
72. Vector(E, E'_4) → v
73. Translate(E, v) → E'_5
74. Translate(E', v) → E''
75. Segment(E'_5, E'') → r_1
76. Line(E, h_1) → s_1
77. Intersect(e_1, s_1, 2) → T
78. Angle(T, E, C) → κ
79. Rotate(E'_5, If[13 < o ≤ 14, ((-(o - 13)) * κ), (-κ)], N) → U
80. Rotate(E'', If[13 < o ≤ 14, ((-(o - 13)) * κ), (-κ)], N) → E'''
81. Segment(U, E''') → t_1
82. Dilate(D, If[5 < o ≤ 6, 6 - o, 0], F) → D'_1
83. Segment(D, D'_1) → a_1
84. Dilate(D, If[5 < o ≤ 6, 6 - o, 0], G) → D'_2
85. Segment(D, D'_2) → b_1
86. Dilate(D, If[14 < o ≤ 15, 15 - o, 0], E''') → D'_3
87. Vector(D, D'_3) → w
88. Translate(D, w) → D'_4
89. Translate(D'_1, w) → S
90. Segment(D'_4, S) → f_2
91. Line(D, i_1) → g_2
92. Intersect(c_1, g_2, 2) → V
93. Angle(V, D, F) → λ
94. Rotate(D'_4, If[15 < o ≤ 16, ((-(o - 15)) * λ), (-λ)], E''') → W
95. Rotate(S, If[15 < o ≤ 16, ((-(o - 15)) * λ), (-λ)], E''') → S'
96. Segment(W, S') → h_2
97. Circle(O, t_1 + h_2) → c_2
98. Intersect(c_2, i_1, 2) → Z
99. Circle(O, 1) → d_2
100. Circle(Z, 1) → e_2
101. Intersect(d_2, i_1, 1) → A_1
102. Intersect(e_2, i_1, 2) → B_1
103. Ray(O, A_1) → i_2
104. Ray(Z, B_1) → j_2
105. Circle(O, q_1) → k_2
106. Intersect(k_2, i_1, 2) → C_1
107. Circle(C_1, n_1) → p_2
108. Intersect(i_1, j_2) → D_1
109. Intersect(i_1, j_2) → E_1
110. Intersect(p_2, i_1) → F_1, G_1
111. Ray(O, A_1) → l_2
112. Segment(N, S') → m_2
113. Dilate(N, If[16 < o ≤ 17, 17 - o, 0], O) → N'
114. Vector(N, N') → u_1
115. Translate(N, u_1) → N'_1
116. Translate(S', u_1) → S''
117. Segment(N'_1, S'') → n_2
118. Segment(N, N'_1) → q_2
119. Segment(O, C_1) → r_2
120. Segment(C_1, Z) → s_2
121. Circle(G_1, 1) → t_2
122. Intersect(t_2, j_2, 2) → H_1
123. Ray(G_1, H_1) → a_2
124. Segment(Z, G_1) → b_2
125. Dilate(O, If[17 < o ≤ 18, 18 - o, 0], Z) → O'
126. Vector(O, O') → v_1
127. Translate(N, v_1) → N'_2
128. Translate(N'_1, v_1) → I_1
129. Segment(N'_2, I_1) → f_3
130. Dilate(R, If[18 < o ≤ 19, 19 - o, 0], O) → R'
131. Vector(R, R') → w_1
132. Translate(E, w_1) → E'_6
133. Translate(E'_3, w_1) → J_1
134. Segment(E'_6, J_1) → g_3
135. Line(R, h_1) → h_3
136. Intersect(e_1, h_3, 2) → K_1
137. Angle(E, R, K_1) → μ
138. Rotate(E'_6, If[19 < o ≤ 20, ((o - 19) * μ), μ], O) → L_1
139. Rotate(J_1, If[19 < o ≤ 20, ((o - 19) * μ), μ], O) → M_1
140. Segment(L_1, M_1) → i_3
141. Dilate(E, If[20 < o ≤ 21, 21 - o, 0], C_1) → E'_7
142. Vector(E, E'_7) → u_2
143. Translate(E, u_2) → E'_8
144. Translate(E'_1, u_2) → N_1
145. Segment(E'_8, N_1) → j_3
146. Angle(T, E, P) → τ
147. Rotate(E'_8, If[21 < o ≤ 22, ((-(o - 21)) * τ), (-τ)], C_1) → O_1
148. Rotate(N_1, If[21 < o ≤ 22, ((-(o - 21)) * τ), (-τ)], C_1) → P_1
149. Segment(O_1, P_1) → k_3
150. Intersect(e_1, s_1, 1) → Q_1
151. Segment(Z, G_1) → m_3
152. Segment(C_1, Z) → n_3
153. Dilate(E, If[22 < o ≤ 23, 23 - o, 0], G_1) → E'_9
154. Vector(E, E'_9) → v_2
155. Translate(E, v_2) → E'_{10}
156. Translate(E'_2, v_2) → R_1
157. Segment(E'_{10}, R_1) → p_3
158. Angle(Q, E, Q_1) → χ
159. Rotate(E'_{10}, If[23 < o ≤ 24, ((o - 23) * χ), χ], G_1) → S_1
160. Rotate(R_1, If[23 < o ≤ 24, ((o - 23) * χ), χ], G_1) → T_1
161. Segment(S_1, T_1) → q_3
162. Polygon(A, B, C) → poly1, c_3, a_3, b_3