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三角形内心构造

三角形内心构造
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2020-06-28 21:33
测试改名0角几何作图
本范例演示如何构造三角形的内心。涉及的核心数学概念包括角平分线和圆的性质。通过使用GeoGebra命令如Segment, Circle, Point, Rotate等，可以清晰地展示作图过程。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Segment(N_1, N_2) → b_1
  2. Circle(A_1, A_0) → c
  3. Circle(B_1, B_0) → d
  4. Circle(C_1, C_0) → e
  5. Point(c) → A
  6. Point(d) → B
  7. Point(e) → C
  8. Segment(C, A) → f
  9. Segment(B, A) → g
  10. Segment(B, C) → h
  11. Circle(A, r_b) → k
  12. Rotate(B, b_d, A) → B'
  13. Angle(B, A, B') → α
  14. Rotate(B, (-b_d), A) → B'_1
  15. Angle(B'_1, A, B) → β
  16. Rotate(C, b_d, A) → C'
  17. Angle(C, A, C') → γ
  18. Rotate(C, (-b_d), A) → C'_1
  19. Angle(C'_1, A, C) → δ
  20. Segment(C'_1, A) → i
  21. Segment(C', A) → j
  22. Segment(B', A) → l
  23. Segment(B'_1, A) → m
  24. Intersect(k, j) → D,
  25. Intersect(k, i) → E,
  26. Intersect(k, l) → F,
  27. Intersect(k, m) → G,
  28. CircleArc(A, G, F) → p
  29. CircleArc(A, E, D) → q
  30. Intersect(p, g) → H,
  31. Intersect(q, f) → I,
  32. Circle(H, r_b) → s
  33. Circle(I, r_b) → t_1
  34. Intersect(s, t_1, 2) → A_b
  35. Rotate(A_b, b_d, H) → J
  36. Angle(A_b, H, J) → ε
  37. Rotate(A_b, (-b_d), H) → K
  38. Angle(K, H, A_b) → ζ
  39. Rotate(A_b, b_d, I) → L
  40. Angle(A_b, I, L) → η
  41. Rotate(A_b, (-b_d), I) → M
  42. Angle(M, I, A_b) → θ
  43. CircleArc(H, K, J) → c_1
  44. CircleArc(I, M, L) → d_1
  45. Segment(N, O) → g_1
  46. Distance(N, O) → NO
  47. Point(Path_d) → Delay_1
  48. Segment(P, Q) → i_1
  49. Point(Path_e) → Delay_2
  50. Segment(R, S) → b
  51. Point(Path_f) → Delay_3
  52. Ray(A, A_b) → l_1
  53. Segment(T, U) → m_1
  54. Point(Path_g) → Delay_4
  55. Point(p) → A_R
  56. CircleArc(A, G, A_R) → t
  57. Segment(A, A_R) → q_1
  58. Point(q) → A_L
  59. CircleArc(A, E, A_L) → s_1
  60. Segment(A_L, A) → f_2
  61. Point(c_1) → I_R
  62. Segment(I_R, H) → g_2
  63. CircleArc(H, K, I_R) → c_2
  64. Point(d_1) → H_R
  65. Segment(I, H_R) → h_2
  66. CircleArc(I, M, H_R) → e_2
  67. Circle(B, r_b) → e_1
  68. Intersect(e_1, h) → V,
  69. Intersect(e_1, g) → W,
  70. Rotate(V, b_d, B) → V'
  71. Angle(V, B, V') → ι
  72. Rotate(V, (-b_d), B) → V'_1
  73. Angle(V'_1, B, V) → κ
  74. Rotate(W, b_d, B) → W'
  75. Angle(W, B, W') → λ
  76. Rotate(W, (-b_d), B) → W'_1
  77. Angle(W'_1, B, W) → μ
  78. CircleArc(B, V'_1, V') → f_1
  79. CircleArc(B, W'_1, W') → h_1
  80. Circle(V, r_b) → p_1
  81. Circle(W, r_b) → k_2
  82. Intersect(p_1, k_2, 2) → B_b
  83. Rotate(B_b, b_d, V) → Z
  84. Angle(B_b, V, Z) → ν
  85. Rotate(B_b, (-b_d), V) → D_1
  86. Angle(D_1, V, B_b) → ξ
  87. Rotate(B_b, b_d, W) → E_1
  88. Angle(B_b, W, E_1) → ο
  89. Rotate(B_b, (-b_d), W) → F_1
  90. Angle(F_1, W, B_b) → ρ
  91. CircleArc(W, F_1, E_1) → p_2
  92. CircleArc(V, D_1, Z) → q_2
  93. Ray(B, B_b) → a_1
  94. Intersect(l_1, a_1) → G_1
  95. Point(Path_h) → Delay_5
  96. Circle(C, r_b) → r_2
  97. Intersect(r_2, f) → H_1,
  98. Intersect(r_2, h) → I_1,
  99. Rotate(H_1, b_d, C) → J_1
  100. Angle(H_1, C, J_1) → σ
  101. Rotate(H_1, (-b_d), C) → K_1
  102. Angle(K_1, C, H_1) → τ
  103. Rotate(I_1, b_d, C) → L_1
  104. Angle(I_1, C, L_1) → υ
  105. Rotate(I_1, (-b_d), C) → M_1
  106. Angle(M_1, C, I_1) → ϕ
  107. CircleArc(C, K_1, J_1) → s_2
  108. CircleArc(C, M_1, L_1) → t_2
  109. Circle(H_1, r_b) → c_3
  110. Circle(I_1, r_b) → d_3
  111. Intersect(c_3, d_3, 2) → B_c
  112. Rotate(B_c, b_d, H_1) → O_1
  113. Angle(B_c, H_1, O_1) → χ
  114. Rotate(B_c, (-b_d), H_1) → P_1
  115. Angle(P_1, H_1, B_c) → ψ
  116. Rotate(B_c, b_d, I_1) → Q_1
  117. Angle(B_c, I_1, Q_1) → ω
  118. Rotate(B_c, (-b_d), I_1) → R_1
  119. Angle(R_1, I_1, B_c) → α_1
  120. CircleArc(I_1, R_1, Q_1) → e_3
  121. CircleArc(H_1, P_1, O_1) → f_3
  122. Ray(C, B_c) → l_2
  123. Segment(O_2, O_3) → m_2
  124. Point(Path_i) → Delay_6
  125. Segment(P_2, P_3) → n_2
  126. Point(Path_j) → Delay_7
  127. Segment(Q_2, Q_3) → g_3
  128. Segment(R_2, R_3) → h_3
  129. Segment(S_2, S_3) → i_3
  130. Point(Path_k) → Delay_8
  131. Point(Path_l) → Delay_9
  132. Point(Path_m) → Delay_10
  133. Segment(T_2, T_3) → j_3
  134. Point(Path_n) → Delay_11
  135. OrthogonalLine(G_1, h) → p_3
  136. OrthogonalLine(G_1, g) → q_3
  137. OrthogonalLine(G_1, f) → r_3
  138. Intersect(h, p_3) → S_1
  139. Intersect(q_3, g) → T_1
  140. Intersect(f, r_3) → U_1
  141. Segment(G_1, S_1) → s_3
  142. Segment(G_1, T_1) → t_3
  143. Segment(G_1, U_1) → f_4
  144. Angle(G_1, U_1, C) → β_1
  145. Angle(G_1, S_1, B) → γ_1
  146. Angle(G_1, T_1, A) → δ_1
  147. Circle(G_1, U_1) → c_4
  148. Segment(LT, RT) → g_4
  149. Segment(RT, RB) → h_4
  150. Segment(RB, LB) → i_4
  151. Segment(LB, LT) → j_4
  152. Distance(j_4, g_4) → o_3
  153. Distance(LT, LB) → u_3