MathPlotAI Logo MathPlotAI

Incenter and Incircle of a Triangle

Incenter and Incircle of a Triangle
Loading the math board and drawing, please wait…
2017-06-13 04:12
TriangleCircleGeometric Construction
This applet dynamically illustrates the properties of the incenter and incircle of a triangle. Key mathematical concepts include the definition of the incenter and the properties of the incircle. Using GeoGebra commands such as Line, Circle, Incircle, etc., the relationship between the incenter and the incircle can be observed. Suitable for students at the middle school level and above to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. Slope(d) → a
  3. PointIn(c) → C
  4. Line(A, C) → e
  5. Line(B, C) → f
  6. Angle(B, A, C) → α
  7. Angle(A, C, B) → β
  8. Angle(C, B, A) → γ
  9. Segment(A, C) → g
  10. Segment(C, B) → h
  11. Segment(B, A) → i
  12. Min(list1) → j
  13. Circle(C, (0.2 * j)) → q
  14. Circle(A, (0.2 * j)) → p
  15. Circle(B, (0.2 * j)) → k
  16. Intersect(q, f, 2) → D
  17. Intersect(q, e, 1) → E
  18. Intersect(q, e, 2) → F
  19. Intersect(p, e, 2) → G
  20. Intersect(p, d, 1) → H
  21. Intersect(k, f, 2) → I_2
  22. Intersect(k, d, 2) → J
  23. Intersect(d, i) → K
  24. Intersect(d, i) → L
  25. Intersect(k, f, 1) → N
  26. Intersect(p, e, 1) → O
  27. Intersect(p, d, 2) → P
  28. Angle(D, C, E) → δ
  29. Angle(O, A, P) → ε
  30. Angle(J, B, I_2) → η
  31. Angle(G, A, H) → θ
  32. Incircle(A, B, C) → r
  33. Center(r) → I
  34. Line(C, I) → l
  35. Line(A, I) → n
  36. Line(B, I) → s
  37. Intersect(e, s) → R
  38. Intersect(d, l) → S
  39. Intersect(f, n) → T
  40. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  41. Rotate(D, δ / 2, C) → D'
  42. Angle(D, C, D') → κ
  43. Rotate(J, η / 2, B) → J'
  44. Angle(J, B, J') → λ
  45. Ray(C, D') → t
  46. Ray(B, J') → e_1
  47. Rotate(O, ε / 2, A) → O'
  48. Angle(O, A, O') → ι
  49. Ray(A, O') → d_1
  50. Segment(C, S) → f_1
  51. Segment(A, T) → g_1
  52. Segment(B, R) → h_1
  53. Intersect(q, f_1, 1) → U
  54. Intersect(q, f, 1) → V
  55. Intersect(p, g_1, 1) → W
  56. Intersect(k, h_1, 1) → Z
  57. CircleSector(C, E, U) → k_1
  58. CircleSector(A, P, W) → q_1
  59. CircleSector(B, I_2, Z) → p_1
  60. Dilate(C, If[0 < m ≤ 1, 1 - m, 0], S) → C'
  61. Segment(C, C') → i_1
  62. Rotate(k_1, If[1 < m ≤ 2, ((m - 1) * β / 2), β / 2], C) → r_1
  63. Dilate(B, If[2 < m ≤ 3, 3 - m, 0], R) → B'
  64. Segment(B, B') → j_1
  65. Rotate(p_1, If[3 < m ≤ 4, ((m - 3) * γ / 2), γ / 2], B) → s_1
  66. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], T) → A'
  67. Segment(A, A') → l_1
  68. Rotate(q_1, If[5 < m ≤ 6, ((m - 5) * α / 2), α / 2], A) → t_1
  69. OrthogonalLine(I, f) → m_1
  70. OrthogonalLine(I, d) → n_1
  71. OrthogonalLine(I, e) → a_2
  72. Intersect(f, m_1) → M
  73. Intersect(d, n_1) → A_1
  74. Intersect(e, a_2) → B_1
  75. Segment(I, M) → b_2
  76. Circle(M, (0.2 * b_2)) → c_2
  77. Intersect(c_2, f, 1) → C_1
  78. Intersect(c_2, b_2, 1) → D_1
  79. Intersect(c_2, f, 2) → E_1
  80. CircleSector(M, E_1, D_1) → d_2
  81. Dilate(I, If[6 < m ≤ 7, 7 - m, 0], M) → Q'
  82. Segment(I, Q') → e_2
  83. Rotate(d_2, If[7.5 < m ≤ 8.5, ((m - 7.5) * π / 2), 1.5707963267948966], M) → f_2
  84. Segment(I, B_1) → g_2
  85. Segment(I, A_1) → h_2
  86. Circle(B_1, (0.2 * g_2)) → k_2
  87. Circle(A_1, (0.2 * h_2)) → p_2
  88. Intersect(k_2, e, 2) → F_1
  89. Intersect(k_2, g_2, 1) → G_1
  90. Intersect(k_2, e, 1) → H_1
  91. Intersect(p_2, d, 2) → I_1
  92. Intersect(p_2, h_2, 1) → J_1
  93. Intersect(p_2, d, 1) → K_1
  94. Dilate(I, If[8.5 < m ≤ 9.5, 9.5 - m, 0], B_1) → Q'_1
  95. Segment(I, Q'_1) → i_2
  96. CircleSector(B_1, H_1, G_1) → q_2
  97. CircleSector(A_1, I_1, J_1) → r_2
  98. Rotate(q_2, If[10 < m ≤ 11, ((m - 10) * π / 2), 1.5707963267948966], B_1) → s_2
  99. Dilate(I, If[11 < m ≤ 12, 12 - m, 0], A_1) → Q'_2
  100. Segment(I, Q'_2) → j_2
  101. Rotate(r_2, If[12.5 < m ≤ 13.5, ((m - 12.5) * π / 2), 1.5708], A_1) → t_2
  102. Angle(M, I, B_1) → ζ
  103. Angle(B_1, I, A_1) → μ
  104. Angle(A_1, I, M) → ν
  105. Rotate(I, If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q'_3
  106. Rotate(Q', If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q''
  107. Segment(Q'_3, Q'') → l_2
  108. Rotate(Q'_3, If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → L_1
  109. Rotate(Q'', If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → Q'''
  110. Segment(L_1, Q''') → m_2
  111. Rotate(A_1, If[16 < m ≤ 18, ((m - 16) * π), 6.28319], I) → M'
  112. Intersect(m_1, f) → Q
  113. Circle(I, Q) → d_3
  114. Line(A, B) → n_2
  115. CircleArc(I, A_1, M') → c_3