Symmedian Point in Triangles

GeoGebra Commands & Parameters

1. Polygon(M, N, O) → poly3, o, m_1, n
2. Midpoint(m_1) → Midpoint''
3. Midpoint(o) → Midpoint
4. Midpoint(n) → Midpoint'
5. Polygon(P, Q, R) → poly4, r, p, q
6. Midpoint(r) → S
7. Midpoint(q) → T
8. Midpoint(p) → U
9. AngularBisector(P, R, Q) → c_1
10. AngularBisector(Q, P, R) → d_1
11. Segment(Q, T) → Median''
12. Segment(U, P) → Median
13. Segment(S, R) → Median'
14. AngularBisector(P, Q, R) → s
15. Polygon(J, K, L) → poly2, l_1, j_1, k_1
16. Point(k_1) → W
17. Segment(W, K) → j
18. Point(l_1) → G
19. Segment(G, L) → k
20. AngularBisector(J, K, L) → a_1
21. AngularBisector(J, L, K) → b_1
22. AngularBisector(K, J, L) → e_1
23. Mirror(W, a_1) → W'
24. Mirror(K, a_1) → K'
25. Segment(W', K') → Symmedian
26. Mirror(J, e_1) → J'
27. Mirror(G, b_1) → G'
28. Mirror(L, b_1) → L'
29. Segment(G', L') → Symmedian'
30. Midpoint(j_1) → B_1
31. Segment(J, B_1) → t
32. Mirror(J, e_1) → J'_3
33. Mirror(B_1, e_1) → Z
34. Segment(J'_3, Z) → Symmedian''
35. Polygon(J_1, K_1, L_1) → poly2_1, l_2, j_2, k_2
36. Point(k_2) → W_1
37. Segment(W_1, K_1) → j_3
38. Point(l_2) → G_1
39. Segment(G_1, L_1) → k_3
40. AngularBisector(J_1, K_1, L_1) → a_3
41. AngularBisector(J_1, L_1, K_1) → b_2
42. AngularBisector(K_1, J_1, L_1) → e_2
43. Mirror(W_1, a_3) → W'_1
44. Mirror(K_1, a_3) → K'_1
45. Segment(W'_1, K'_1) → Symmedian_1
46. Mirror(G_1, b_2) → G'_1
47. Mirror(L_1, b_2) → L'_1
48. Segment(G'_1, L'_1) → Symmedian'_1
49. Midpoint(j_2) → B_2
50. Segment(J_1, B_2) → t_1
51. Mirror(J_1, e_2) → J'_4
52. Mirror(B_2, e_2) → Z_1
53. Segment(J'_4, Z_1) → t'_1
54. Intersect(l_2, Symmedian'_1) → H
55. Intersect(k_2, Symmedian_1) → V
56. Intersect(j_2, t'_1) → A_1
57. Segment(K_1, V) → f_1
58. Segment(J_1, A_1) → g_1
59. Segment(H, L_1) → h_1
60. Polygon(J_2, K_2, L_2) → poly2_2, l_3, j_4, k_4
61. Point(k_4) → W_2
62. Segment(W_2, K_2) → j_5
63. Point(l_3) → G_2
64. Segment(G_2, L_2) → k_5
65. AngularBisector(J_2, K_2, L_2) → a_2
66. AngularBisector(J_2, L_2, K_2) → b_3
67. AngularBisector(K_2, J_2, L_2) → e_3
68. Mirror(W_2, a_2) → W'_2
69. Mirror(K_2, a_2) → K'_2
70. Segment(W'_2, K'_2) → Symmedian_2
71. Mirror(G_2, b_3) → G'_2
72. Mirror(L_2, b_3) → L'_2
73. Segment(G'_2, L'_2) → Symmedian'_2
74. Midpoint(j_4) → B_3
75. Segment(J_2, B_3) → t_2
76. Mirror(J_2, e_3) → J'_1
77. Mirror(B_3, e_3) → Z_2
78. Segment(J'_1, Z_2) → t'_2
79. Intersect(l_3, Symmedian'_2) → H_1
80. Intersect(k_4, Symmedian_2) → V_1
81. Intersect(j_4, t'_2) → A_2
82. Segment(K_2, V_1) → f_2
83. Segment(J_2, A_2) → g_2
84. Segment(H_1, L_2) → h_2
85. Intersect(f_2, g_2) → SYMMEDIANPOINT
86. Polygon(J_3, K_3, L_3) → poly2_3, l_4, j_6, k_6
87. Point(k_6) → W_3
88. Segment(W_3, K_3) → j_7
89. Point(l_4) → G_3
90. Segment(G_3, L_3) → k_7
91. AngularBisector(J_3, K_3, L_3) → a_4
92. AngularBisector(J_3, L_3, K_3) → b_4
93. AngularBisector(K_3, J_3, L_3) → e_4
94. Mirror(W_3, a_4) → W'_3
95. Mirror(K_3, a_4) → K'_3
96. Segment(W'_3, K'_3) → Symmedian_3
97. Mirror(G_3, b_4) → G'_3
98. Mirror(L_3, b_4) → L'_3
99. Segment(G'_3, L'_3) → Symmedian'_3
100. Midpoint(j_6) → B_4
101. Segment(J_3, B_4) → t_3
102. Mirror(J_3, e_4) → J'_2
103. Mirror(B_4, e_4) → Z_3
104. Segment(J'_2, Z_3) → t'_3
105. Intersect(l_4, Symmedian'_3) → H_2
106. Intersect(k_6, Symmedian_3) → V_2
107. Intersect(j_6, t'_3) → A_3
108. Segment(K_3, V_2) → f_3
109. Segment(J_3, A_3) → g_3
110. Segment(H_2, L_3) → h_3
111. Intersect(f_3, g_3) → SYMMEDIANPOINT'
112. Midpoint(l_4) → B
113. Midpoint(k_6) → C
114. Midpoint(j_6) → D
115. Segment(K_3, C) → a
116. Segment(J_3, D) → b
117. Segment(B, L_3) → c
118. Intersect(a, b) → CENTROID