Circle Theorems

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Point(c) → C
4. Intersect(c, y = 1, 2) → D
5. Segment(C, D) → f
6. Point(c) → E
7. Point(c) → F
8. Segment(E, C) → g
9. Segment(E, D) → h
10. Segment(F, C) → i
11. Segment(F, D) → j
12. Angle(C, E, D) → α
13. Angle(C, F, D) → β
14. Intersect(c_2, y = 2, 2) → G
15. Intersect(c_2, y = 2) → I, K
16. Segment(I, G) → l
17. Point(c_2) → H
18. Segment(H, I) → k
19. Segment(H, K) → m
20. Angle(I, H, K) → γ
21. Point(c_{3}) → M
22. Point(c_{3}) → N
23. Point(c_{3}) → O
24. Segment(M, N) → n
25. Segment(M, O) → p
26. Segment(O, L) → q
27. Segment(L, N) → r
28. Angle(N, M, O) → δ
29. AngularBisector(N, L, O) → s
30. Point(s) → Q
31. Angle(N, L, Q) → ε
32. Angle(Q, L, O) → ζ
33. Angle(N, L, O) → η
34. Segment(L, Q) → t
35. Point(c_{4}) → P
36. Point(c_{4}) → R
37. Segment(P, R) → a
38. Midpoint(a) → T
39. Segment(S, T) → b
40. Angle(S, T, R) → θ
41. Angle(S, T, P) → ι
42. Segment(T, R) → d
43. Segment(T, P) → e
44. Point(c_{5}) → V
45. Segment(U, V) → f_1
46. Point(c_{5}) → W
47. Segment(U, W) → g_1
48. OrthogonalLine(V, f_1) → h_1
49. OrthogonalLine(W, g_1) → i_1
50. Intersect(h_1, i_1) → Z
51. Circle(Z, V) → c_1
52. Circle(V, Z) → d_1
53. Circle(W, Z) → e_1
54. Intersect(d_1, h_1, 2) → A_1
55. Intersect(c_1, h_1, 2) → B_1
56. Segment(A_1, B_1) → j_1
57. Intersect(e_1, i_1, 2) → C_1
58. Intersect(c_1, i_1, 2) → D_1
59. Segment(C_1, D_1) → k_1
60. Segment(W, Z) → l_1
61. Segment(V, Z) → m_1
62. Angle(U, W, Z) → κ
63. Angle(U, V, Z) → λ
64. Point(c_{6}) → J
65. Point(c_{6}) → E_1
66. Point(c_{6}) → F_1
67. Point(c_{6}) → G_1
68. Polygon(J, E_1, F_1, G_1) → q1, j_2, n_1, p_1, q_1
69. Angle(J, E_1, F_1) → μ
70. Angle(J, G_1, F_1) → ν
71. Angle(E_1, J, G_1) → ξ
72. Angle(G_1, F_1, E_1) → ο
73. Point(c_{7}) → I_1
74. Segment(H_1, I_1) → r_1
75. OrthogonalLine(I_1, r_1) → s_1
76. Point(s_1) → J_1
77. Circle(I_1, J_1) → t_1
78. Intersect(t_1, s_1, 2) → K_1
79. Segment(K_1, J_1) → a_1
80. Angle(H_1, I_1, J_1) → ρ
81. Angle(H_1, I_1, K_1) → σ
82. Point(c_{8}) → M_1
83. Segment(L_1, M_1) → b_1
84. OrthogonalLine(M_1, b_1) → f_2
85. Point(f_2) → N_1
86. Circle(M_1, N_1) → d_2
87. Intersect(d_2, f_2, 2) → O_1
88. Segment(N_1, O_1) → g_2
89. Point(c_{8}) → P_1
90. Point(c_{8}) → Q_1
91. Segment(P_1, M_1) → h_2
92. Segment(Q_1, M_1) → i_2
93. Segment(P_1, Q_1) → k_2
94. Angle(P_1, M_1, N_1) → τ
95. Angle(Q_1, M_1, O_1) → υ
96. Angle(M_1, P_1, Q_1) → ϕ
97. Angle(P_1, Q_1, M_1) → χ