X₅₅₂

POINT MAIA I

X₅₅₂ = isogonal conjugate of X₇₀₆₄

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

X₅₅₂ (POINT MAIA I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Trilinears: \(1/[a(b + c - a)(b + c)^{2}] : 1/[b(c +a - b)(c + a)^{2}] : 1/[c(a + b - c)(a + b)^{2}]\)

Barycentrics: \(1/[(b + c - a)(b + c)^{2}] : 1/[(c + a - b)(c + a)^{2}] : 1/[(a + b - c)(a + b)^{2}]\)

Search Value (6, 9, 13): \(0.387544973655\)

▸ Alternate Coordinates1 form

• Barycentrics: \((a + b)^{2} (a + b - c) \cdot (a + c)^{2} (a - b + c) : :\)

X₅₅₂ lies on theselines: {57, 4573}, {86, 40998}, {261, 873}, {553, 1412}, {1088, 4616}, {4633, 30568}, {4637, 33765}, {6628, 7341}

▸ Functional Relations10 relations

• X₅₅₂ = isogonal conjugate of X₇₀₆₄

• X₅₅₂ = isotomic conjugate of X₆₀₅₇

• X₅₅₂ = isotomic conjugate of the isogonal conjugate of X₇₃₄₁

• X₅₅₂ = X_i-cross conjugate of X_j for these (i,j): {757, 1509}, {1358, 17096}, {7203, 4573}, {16714, 274}

• X₅₅₂ = X_i-isoconjugate of X_j for these (i,j): {1, 7064}, {8, 872}, {9, 1500}, {12, 1253}, {31, 6057}, {33, 3690}, {37, 1334}, {41, 594}, {42, 210}, {55, 756}, {181, 200}, {201, 7071}, {212, 7140}, {213, 2321}, {220, 2171}, {284, 762}, {312, 7109}, {480, 1254}, {512, 4069}, {607, 3949}, {644, 4079}, {657, 21859}, {663, 40521}, {798, 30730}, {1018, 3709}, {1089, 2175}, {1109, 6066}, {1110, 4092}, {1400, 4515}, {1402, 4082}, {1802, 8736}, {1824, 2318}, {1918, 3701}, {2194, 6535}, {2197, 7079}, {2205, 30713}, {2212, 3695}, {2333, 3694}, {2643, 6065}, {3063, 4103}, {3208, 6378}, {3939, 4705}, {4041, 4557}, {4095, 40729}, {4171, 4559}, {4524, 4551}, {6354, 6602}, {6358, 14827}, {7035, 7063}, {9447, 28654}, {20665, 43265}, {21816, 33635}

• X₅₅₂ = X_i-Dao conjugate of X_j for these (i,j): {2, 6057}, {3, 7064}, {12, 17113}, {181, 6609}, {210, 40592}, {223, 756}, {478, 1500}, {514, 4092}, {594, 3160}, {762, 40590}, {1089, 40593}, {1214, 6535}, {1334, 40589}, {2321, 6626}, {3700, 40620}, {3701, 34021}, {4024, 40615}, {4069, 39054}, {4082, 40605}, {4103, 10001}, {4515, 40582}, {4705, 40617}, {4778, 31890}, {7140, 40837}, {21673, 38930}, {30730, 31998}

• X₅₅₂ = cevapoint of X_i and X_j for these (i,j): {6, 16691}, {1014, 1434}, {1358, 17096}

• X₅₅₂ = trilinear pole of line {17096, 30724}

• X₅₅₂ = barycentric product X_i*X_j for these {i,j}: {7, 1509}, {57, 873}, {76, 7341}, {85, 757}, {86, 1434}, {99, 17096}, {226, 6628}, {261, 279}, {274, 1014}, {310, 1412}, {479, 7058}, {593, 6063}, {763, 1441}, {799, 7203}, {849, 20567}, {1019, 4625}, {1086, 7340}, {1088, 2185}, {1098, 23062}, {1357, 34537}, {1358, 4590}, {1407, 18021}, {1408, 6385}, {1414, 7199}, {1502, 7342}, {3669, 4623}, {3676, 4610}, {3737, 4635}, {4560, 4616}, {4573, 7192}, {4620, 17205}, {4631, 43932}, {4637, 18155}, {7055, 36419}, {7056, 46103}, {7196, 7303}, {7248, 7307}

• X₅₅₂ = barycentric quotient X_i/X_j for these {i,j}: {2, 6057}, {6, 7064}, {7, 594}, {21, 4515}, {56, 1500}, {57, 756}, {58, 1334}, {60, 220}, {65, 762}, {77, 3949}, {81, 210}, {85, 1089}, {86, 2321}, {99, 30730}, {222, 3690}, {226, 6535}, {249, 6065}, {261, 346}, {269, 2171}, {270, 7079}, {274, 3701}, {278, 7140}, {279, 12}, {310, 30713}, {331, 7141}, {333, 4082}, {348, 3695}, {479, 6354}, {553, 8013}, {593, 55}, {604, 872}, {651, 40521}, {662, 4069}, {664, 4103}, {738, 1254}, {757, 9}, {763, 21}, {849, 41}, {873, 312}, {934, 21859}, {1014, 37}, {1019, 4041}, {1086, 4092}, {1088, 6358}, {1098, 728}, {1119, 8736}, {1357, 3124}, {1358, 115}, {1396, 1824}, {1397, 7109}, {1407, 181}, {1408, 213}, {1412, 42}, {1414, 1018}, {1434, 10}, {1443, 4053}, {1444, 3694}, {1447, 4037}, {1509, 8}, {1790, 2318}, {1977, 7063}, {2150, 1253}, {2185, 200}, {2189, 7071}, {3669, 4705}, {3674, 20653}, {3676, 4024}, {3733, 3709}, {3737, 4171}, {3946, 21673}, {4556, 3939}, {4565, 4557}, {4573, 3952}, {4590, 4076}, {4610, 3699}, {4612, 4578}, {4616, 4552}, {4623, 646}, {4625, 4033}, {4626, 4605}, {4637, 4551}, {6063, 28654}, {6354, 6058}, {6628, 333}, {7053, 2197}, {7054, 480}, {7056, 26942}, {7058, 5423}, {7153, 7148}, {7175, 21803}, {7176, 21021}, {7177, 201}, {7185, 16886}, {7192, 3700}, {7199, 4086}, {7203, 661}, {7252, 4524}, {7304, 27538}, {7340, 1016}, {7341, 6}, {7342, 32}, {8025, 4046}, {16705, 3704}, {16726, 4516}, {16947, 1918}, {17074, 14973}, {17095, 7206}, {17096, 523}, {17103, 4095}, {17205, 21044}, {17206, 3710}, {17212, 4140}, {17474, 21704}, {18164, 21039}, {18166, 4111}, {18191, 36197}, {18600, 21031}, {23357, 6066}, {24002, 4036}, {24471, 21810}, {26856, 4081}, {30097, 21713}, {30576, 3689}, {30581, 3683}, {30593, 3686}, {30682, 6356}, {30724, 6367}, {32636, 21816}, {33295, 3985}, {33947, 4136}, {36419, 1857}, {36420, 6059}, {38859, 20616}, {40153, 40966}, {41777, 7237}, {42028, 4061}, {43924, 4079}, {46103, 7046}