X₃₆₉₂

X₁₇₂₃com(EXTOUCH TRIANGLE)

X₃₆₉₂ = X₁-zayin conjugate of X₁₄₃₅

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

X₃₆₉₂ (X₁₇₂₃com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 9}, {63, 69}

• Related Centers: X₁₄₃₅ (-BETH CONJUGATE OF X₂₇₈), X₈ (NAGEL POINT), X₉ (MITTENPUNKT), X₆₃ (ISOGONAL CONJUGATE OF X₁₉), X₆₉ (SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE)

Trilinears: \(\cot A \cot^{2}(A/2) : :\) (Peter Moses, 12/19/11)

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

Search Value (6, 9, 13): \(5.925164805070\)

▸ Alternate Coordinates1 form

• Barycentrics: \((1 + \cos A)(1 - \sec A) : :\)

▸ Incident Central Lines45 lines

{1, 1257}, {6, 3693}, {8, 9}, {19, 5174}, {37, 4513}, {40, 5279}, {48, 4855}, {57, 4869}, {63, 69}, {78, 219}, {100, 610}, {145, 2257}, {190, 322}, {200, 1253}, {220, 3965}, {268, 271}, {281, 6735}, {282, 2057}, {312, 3305}, {326, 1332}, {341, 2322}, {380, 3871}, {519, 1723}, {579, 4684}, {595, 1743}, {644, 2324}, {1018, 1766}, {1034, 7080}, {1073, 3998}, {1229, 4384}, {1441, 3729}, {1445, 3912}, {1792, 1802}, {1809, 2289}, {2264, 3913}, {2285, 3501}, {2897, 3882}, {3436, 8804}, {3713, 4515}, {3731, 9623}, {3926, 7177}, {3949, 3984}, {3951, 4047}, {4073, 4319}, {10325, 10860}

▸ Functional Relations13 relations

• X₃₆₉₂ = isogonal conjugate of X₁₄₃₅

• X₃₆₉₂ = isotomic conjugate of X₁₈₄₇

• X₃₆₉₂ = crosspoint of X_i and X_j for these (i,j): {345, 1265}, {765, 1332}, {1016, 7256}

• X₃₆₉₂ = crosssum of X_i and X_j for these (i,j): {244, 6591}, {608, 1398}, {1015, 7250}

• X₃₆₉₂ = X_i-cross conjugate of X_j for these (i,j): {1260, 78}, {1802, 200}, {3694, 3692}

• X₃₆₉₂ = X_i-Ceva conjugate of X_j for these (i,j): {341, 200}, {345, 78}, {765, 4578}, {1792, 1260}

• X₃₆₉₂ = X_i-beth conjugate of X_j for these (i,j): {345, 6350}, {644, 1766}, {1332, 7013}, {3692, 219}, {6558, 3692}, {7259, 2324}

• X₃₆₉₂ = X₄₄₆₂-gimel conjugate of X₃₆₉₂

• X₃₆₉₂ = X₁-zayin conjugate of X₁₄₃₅

• X₃₆₉₂ = excentral-to-ABC barycentric image of X₁₇₂₃

• X₃₆₉₂ = isoconjugate of X_j and X_j for these (i,j): {1, 1435}, {2, 1398}, {4, 1407}, {6, 1119}, {7, 608}, {19, 269}, {25, 279}, {27, 1042}, {28, 1427}, {31, 1847}, {33, 738}, {34, 57}, {56, 278}, {65, 1396}, {81, 1426}, {85, 1395}, {92, 1106}, {108, 3669}, {158, 7099}, {162, 7216}, {196, 1413}, {208, 1422}, {222, 1118}, {225, 1412}, {244, 7128}, {270, 7147}, {273, 604}, {281, 7023}, {318, 7366}, {331, 1397}, {348, 7337}, {393, 7053}, {479, 607}, {648, 7250}, {667, 13149}, {934, 6591}, {1014, 1880}, {1088, 1973}, {1096, 7177}, {1262, 2969}, {1358, 7115}, {1416, 5236}, {1439, 5317}, {1440, 3209}, {1446, 2203}, {1461, 7649}, {1462, 1876}, {1474, 3668}, {2189, 6046}, {2207, 7056}, {2221, 7103}, {2489, 4616}, {3064, 6614}, {3213, 8809}, {6612, 7952}, {7339, 8735}, {7341, 8736}

• X₃₆₉₂ = barycentric product X_i*X_j for these {i,j}: {1, 1265}, {3, 341}, {8, 78}, {9, 345}, {10, 1792}, {21, 3710}, {33, 1264}, {55, 3718}, {63, 346}, {69, 200}, {72, 1043}, {75, 1260}, {76, 1802}, {77, 5423}, {210, 332}, {212, 3596}, {219, 312}, {220, 304}, {271, 7080}, {281, 3719}, {283, 3701}, {305, 1253}, {306, 2287}, {314, 2318}, {318, 1259}, {321, 2327}, {326, 7046}, {333, 3694}, {348, 728}, {394, 7101}, {480, 7182}, {521, 3699}, {522, 4571}, {525, 7259}, {644, 6332}, {645, 8611}, {646, 652}, {647, 7258}, {656, 7256}, {765, 2968}, {905, 6558}, {1098, 3695}, {1331, 4397}, {1332, 3239}, {1444, 4082}, {1809, 6735}, {1812, 2321}, {2289, 7017}, {2322, 3998}, {3270, 7035}, {3900, 4561}, {3926, 7079}, {3949, 7058}, {4025, 4578}, {4076, 7004}, {4163, 6516}, {4171, 4563}, {4391, 4587}, {4855, 6556}

• X₃₆₉₂ = barycentric quotient X_i/X_j for these {i,j}: {1, 1119}, {2, 1847}, {3, 269}, {6, 1435}, {8, 273}, {9, 278}, {31, 1398}, {33, 1118}, {41, 608}, {42, 1426}, {48, 1407}, {55, 34}, {63, 279}, {69, 1088}, {71, 1427}, {72, 3668}, {77, 479}, {78, 7}, {184, 1106}, {190, 13149}, {200, 4}, {201, 6046}, {210, 225}, {212, 56}, {219, 57}, {220, 19}, {222, 738}, {228, 1042}, {255, 7053}, {268, 1422}, {271, 1440}, {283, 1014}, {284, 1396}, {306, 1446}, {312, 331}, {326, 7056}, {341, 264}, {345, 85}, {346, 92}, {394, 7177}, {480, 33}, {521, 3676}, {577, 7099}, {603, 7023}, {612, 7103}, {644, 653}, {647, 7216}, {652, 3669}, {657, 6591}, {728, 281}, {810, 7250}, {906, 1461}, {1038, 7197}, {1040, 7195}, {1043, 286}, {1252, 7128}, {1253, 25}, {1259, 77}, {1260, 1}, {1264, 7182}, {1265, 75}, {1331, 934}, {1332, 658}, {1334, 1880}, {1792, 86}, {1802, 6}, {1812, 1434}, {1813, 4617}, {2175, 1395}, {2188, 1413}, {2193, 1412}, {2197, 7147}, {2212, 7337}, {2287, 27}, {2289, 222}, {2310, 2969}, {2318, 65}, {2324, 196}, {2327, 81}, {2328, 28}, {2332, 5317}, {2340, 1876}, {2638, 3937}, {2968, 1111}, {3119, 8735}, {3270, 244}, {3682, 1439}, {3689, 1877}, {3690, 1254}, {3693, 5236}, {3694, 226}, {3710, 1441}, {3713, 5307}, {3718, 6063}, {3719, 348}, {3781, 7204}, {3900, 7649}, {3939, 108}, {3949, 6354}, {3965, 1848}, {4055, 1410}, {4130, 3064}, {4171, 2501}, {4183, 8747}, {4319, 1851}, {4420, 7282}, {4433, 1874}, {4515, 1826}, {4558, 4637}, {4561, 4569}, {4563, 4635}, {4571, 664}, {4574, 1020}, {4578, 1897}, {4587, 651}, {4592, 4616}, {5227, 7365}, {5423, 318}, {6056, 603}, {6061, 270}, {6065, 7012}, {6516, 4626}, {6558, 6335}, {6602, 607}, {7004, 1358}, {7046, 158}, {7071, 1096}, {7074, 208}, {7079, 393}, {7080, 342}, {7085, 4320}, {7101, 2052}, {7256, 811}, {7258, 6331}, {7259, 648}, {7367, 7129}, {7368, 2331}, {8611, 7178}, {11517, 4341}