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Incenter Construction of a Triangle

Incenter Construction of a Triangle
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2020-06-28 21:33
TriangleAngleGeometric Construction
This example demonstrates the construction of the incenter of a triangle. Key mathematical concepts include angle bisectors and circle properties. Using GeoGebra commands such as Segment, Circle, Point, Rotate, etc., the construction process is clearly illustrated. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  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