X₁₀₆

Λ(INCENTER, CENTROID)

X₁₀₆ = anticomplement of X₁₂₁

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₀₆ (Λ(INCENTER, CENTROID)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1293, 3}

• Related Centers: X₁₂₉₃ (COLLINGS TRANSFORM OF X₁₂₁), X₃ (CIRCUMCENTER)

Trilinears: \(a/(2a - b - c) : b/(2b - c - a) : c/(2c - a -b)\)

Barycentrics: \(a^{2}/(2a - b - c) : b^{2}/(2b - c - a) : c^{2}/(2c - a - b)\)

Tripolars: \(|b c (2 a - b - c)| : :\)

Search Value (6, 9, 13): \(0.410148388324\)

▸ Incident Central Lines245 lines

{1, 88}, {2, 121}, {3, 1293}, {4, 5510}, {5, 10744}, {6, 101}, {10, 1222}, {11, 10774}, {20, 34548}, {21, 34594}, {25, 9088}, {30, 2692}, {31, 2163}, {32, 30554}, {34, 108}, {35, 28218}, {36, 901}, {39, 9327}, {40, 14664}, {41, 9336}, {42, 16057}, {55, 5577}, {56, 109}, {58, 110}, {74, 2776}, {80, 1647}, {86, 99}, {87, 932}, {98, 2789}, {102, 2815}, {103, 2424}, {104, 1769}, {105, 1022}, {107, 2839}, {111, 2843}, {112, 1474}, {172, 28864}, {182, 28564}, {187, 2702}, {190, 34587}, {238, 898}, {269, 934}, {291, 5376}, {292, 813}, {347, 1305}, {386, 2334}, {476, 7478}, {511, 2705}, {512, 2712}, {513, 2718}, {514, 2726}, {515, 2731}, {516, 2737}, {517, 2743}, {518, 2748}, {519, 1120}, {520, 2755}, {521, 2756}, {522, 2757}, {523, 2758}, {524, 2759}, {525, 2760}, {535, 19634}, {572, 28467}, {614, 998}, {649, 2384}, {663, 840}, {664, 21208}, {665, 2291}, {667, 2382}, {672, 6017}, {675, 6548}, {691, 1326}, {693, 2863}, {726, 4582}, {727, 23355}, {739, 8632}, {789, 870}, {833, 977}, {835, 3616}, {905, 2751}, {919, 1055}, {927, 1323}, {931, 4658}, {952, 3756}, {953, 1459}, {958, 3038}, {979, 8666}, {991, 28291}, {997, 16496}, {1001, 29351}, {1068, 26704}, {1086, 1387}, {1125, 1220}, {1126, 1193}, {1130, 3659}, {1145, 24864}, {1168, 1319}, {1191, 28162}, {1203, 28176}, {1279, 1308}, {1290, 37919}, {1292, 2191}, {1294, 9524}, {1295, 9525}, {1296, 9526}, {1297, 9527}, {1309, 1785}, {1310, 16491}, {1350, 28295}, {1384, 26716}, {1385, 6011}, {1386, 8691}, {1413, 4306}, {1431, 29055}, {1457, 2720}, {1458, 14733}, {1462, 23890}, {1464, 34921}, {1468, 8652}, {1480, 10269}, {1616, 8699}, {1724, 28370}, {1739, 6095}, {1795, 35011}, {1914, 28875}, {1960, 4491}, {1964, 29189}, {2112, 28895}, {2215, 36080}, {2241, 28907}, {2275, 28883}, {2279, 8693}, {2280, 28911}, {2297, 3731}, {2308, 28180}, {2342, 19619}, {2390, 35186}, {2403, 9083}, {2441, 8659}, {2703, 17954}, {2716, 6129}, {2734, 21172}, {2742, 13329}, {2983, 29163}, {3098, 28469}, {3120, 16173}, {3226, 4555}, {3227, 3570}, {3242, 35272}, {3295, 8572}, {3333, 15839}, {3582, 36590}, {3699, 6789}, {3746, 8698}, {3898, 17596}, {3915, 8697}, {3939, 22560}, {3973, 33589}, {3976, 30144}, {4251, 28852}, {4252, 28192}, {4262, 28847}, {4432, 24416}, {4511, 4694}, {4615, 9150}, {4622, 16481}, {4677, 9350}, {4738, 9457}, {4752, 20331}, {4803, 31136}, {4867, 17449}, {4945, 25055}, {5024, 6184}, {5053, 8610}, {5092, 28486}, {5127, 6083}, {5258, 28352}, {5272, 9104}, {5288, 27627}, {5297, 31514}, {5400, 38669}, {5526, 5548}, {6010, 37508}, {6013, 10013}, {6099, 36052}, {6551, 9268}, {6575, 10579}, {6577, 34444}, {6765, 7963}, {7191, 9070}, {7208, 9318}, {7290, 14074}, {7312, 17960}, {7373, 28226}, {8028, 24858}, {8643, 9097}, {8658, 28302}, {8686, 37627}, {8688, 12513}, {8692, 11194}, {9067, 37670}, {9086, 36887}, {9093, 23598}, {9624, 36939}, {10179, 37599}, {10199, 37716}, {10571, 36082}, {10703, 12740}, {10987, 28868}, {11249, 34430}, {11636, 34476}, {13397, 28011}, {14028, 21630}, {14422, 23352}, {14438, 26278}, {14996, 27950}, {15306, 37541}, {15325, 17734}, {15663, 22770}, {15955, 20323}, {16466, 28148}, {16796, 32682}, {16801, 30664}, {16969, 24047}, {16971, 25426}, {17461, 17595}, {17724, 34123}, {18047, 27195}, {18976, 34355}, {21008, 28856}, {21842, 28082}, {22744, 29038}, {22837, 24174}, {23675, 24160}, {24516, 32454}, {24625, 37680}, {25920, 26698}, {26711, 38458}, {28096, 37710}, {28528, 33878}, {28552, 37517}, {28584, 30269}, {29227, 36598}, {34977, 37592}

▸ Functional Relations31 relations

• X₁₀₆ = reflection of X₁₂₉₃ in X₃

• X₁₀₆ = isogonal conjugate of X₅₁₉

• X₁₀₆ = isotomic conjugate of X₃₂₆₄

• X₁₀₆ = complement of X₂₁₂₉₀

• X₁₀₆ = anticomplement of X₁₂₁

• X₁₀₆ = X₃₆-cross conjugate of X₅₈

• X₁₀₆ = X_i-beth conjugate of X_j for these (i,j): (21, 100), (901, 106)

• X₁₀₆ = Λ(X₁, X₂)

• X₁₀₆ = X₁₂₂-of-hexyl-triangle

• X₁₀₆ = trilinear pole of line X₆X₆₄₉

• X₁₀₆ = Ψ(X_i, X_j) for these (i,j): (1, 513), (2, 514), (6, 649), (9, 650), (100, 1), (101, 6), (190, 2), (651, 57)

• X₁₀₆ = trilinear pole wrt 2nd circumperp triangle of line X₁X₆

• X₁₀₆ = X₁₀₇ of 2nd circumperp triangle

• X₁₀₆ = trilinear pole wrt circumsymmedial triangle of line X₆X₃₁

• X₁₀₆ = reflection of X₂₇₅₈ in the Euler line

• X₁₀₆ = reflection of X₂₇₁₂ in the Brocard axis

• X₁₀₆ = reflection of X₂₇₁₈ in line X₁X₃

• X₁₀₆ = X₆-isoconjugate of X₄₃₅₈

• X₁₀₆ = X₁₃₃-of-excentral triangle

• X₁₀₆ = barycentric product of PU(50)

• X₁₀₆ = trilinear product of PU(98)

• X₁₀₆ = eigencenter of 1st circumperp triangle

• X₁₀₆ = Thomson-isogonal conjugate of X₃₆₆₇

• X₁₀₆ = Lucas-isogonal conjugate of X₃₆₆₇

• X₁₀₆ = polar conjugate of isogonal conjugate of X₃₂₆₅₉

• X₁₀₆ = trilinear product of circumcircle intercepts of line X₁X₅₁₃

• X₁₀₆ = trilinear pole, wrt Thomson triangle, of line X₁₂₀₁X₂₁₇₇

• X₁₀₆ = Conway-circle-inverse of X₃₅₆₃₆

• X₁₀₆ = polar conjugate of isotomic conjugate of X₁₇₉₇

• X₁₀₆ = X₆₃-isoconjugate of X₈₇₅₆

• X₁₀₆ = X₁-Ceva conjugate of X₃₉₁₄₈