X1385

MIDPOINT OF INCENTER AND CIRCUMCENTER

X1385 is the midpoint of incenter and circumcenter.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 21, 104 }: Central Line L(21, 104) { 54, 72 }: Central Line L(54, 72) { 10, 140 }: Central Line L(10, 140) { 2, 355 }: Central Line L(2, 355) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_54 = KOSNITA POINT (0.5880, 0.2176) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_2 = CENTROID (0.5374, 0.2000) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_1385 = MIDPOINT OF INCENTER AND CIRCUMCENTER (0.5357, 0.1677) A B C X1 X3 X21 X104 X54 X72 X10 X140 X2 X355 X1385 (a, b, c) = (5, 6, 7) | AB = 1

X1385 (MIDPOINT OF INCENTER AND CIRCUMCENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(16(\operatorname{area} ABC)^{2} + a(a + b + c)(b^{2} + c^{2} - a^{2}) : :\)
Barycentrics: \(a (2 a^{3} - a^{2} b - 2 a b^{2} + b^{3} - a^{2} c + 2 a b c - b^{2} c - 2 a c^{2} - b c^{2} + c^{3}) : :\)
Search Value (6, 9, 13): \(4.236335701827\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(2 \cos A + \cos B + \cos C - 1 : :\)

  • Trilinears: \(r + R \cos A : :\)

▸ Linear Combinations1 combination

  • X1385 = X1 + X3 = \(3\) X1 + X40, \(5\) X1 + \(3\) X165, \(3\) X1 - X1482, X1 + \(3\) X3576, \(2\) X1 + X3579, \(5\) X1 - X7982, \(3\) X1 + \(5\) X7987, \(7\) X1 + X7991, \(7\) X1 - X8148, X1 - \(3\) X10246, \(5\) X1 - \(3\) X10247, \(11\) X1 - \(3\) X11224, \(4\) X1 - X11278, \(9\) X1 - X11531, \(5\) X1 + X12702, X1 + \(2\) X13624, \(13\) X1 - \(5\) X16189, \(25\) X1 - \(9\) X16191, \(9\) X1 + \(7\) X16192, \(7\) X1 - \(3\) X16200, \(2\) X1 + \(3\) X17502, X1 + \(7\) X30389, X1 - \(9\) X30392, X1 + \(6\) X31662, \(3\) X1 + \(2\) X31663, \(2\) X1 + \(5\) X31666, \(3\) X1 - \(2\) X33179, \(7\) X1 + \(5\) X35242, \(3\) X1 - \(5\) X37624, \(3\) X3 - X40, \(5\) X3 - \(3\) X165, \(3\) X3 + X1482, X3 - \(3\) X3576, \(5\) X3 + X7982, \(3\) X3 - \(5\) X7987, \(7\) X3 - X7991, \(7\) X3 + X8148, \(2\) X3 + X10222, X3 + \(3\) X10246, \(5\) X3 + \(3\) X10247, \(11\) X3 + \(3\) X11224, \(4\) X3 + X11278, \(9\) X3 + X11531, \(5\) X3 - X12702, X3 + \(2\) X15178, \(13\) X3 + \(5\) X16189, \(25\) X3 + \(9\) X16191, \(9\) X3 - \(7\) X16192, \(7\) X3 + \(3\) X16200, \(2\) X3 - \(3\) X17502, X3 - \(7\) X30389, X3 + \(9\) X30392, X3 - \(6\) X31662, \(3\) X3 - \(2\) X31663, and many others

X1385 lies on the cubics K798 and K981.

▸ Incident Central Lines905 lines

{1, 3}, {2, 355}, {4, 1538}, {5, 515}, {6, 9619}, {7, 38030}, {8, 631}, {9, 20818}, {10, 140}, {11, 6842}, {12, 6882}, {20, 3622}, {21, 104}, {24, 1829}, {28, 1871}, {29, 39529}, {30, 551}, {37, 572}, {41, 43065}, {48, 40937}, {54, 72}, {63, 5730}, {71, 17438}, {73, 34586}, {74, 5606}, {77, 945}, {78, 956}, {79, 4325}, {80, 17606}, {92, 7531}, {98, 29299}, {100, 4861}, {101, 1212}, {102, 7100}, {106, 6011}, {119, 4187}, {142, 37281}, {145, 3523}, {149, 11015}, {150, 17095}, {153, 37162}, {169, 3207}, {182, 518}, {186, 41722}, {191, 28443}, {210, 5258}, {215, 17660}, {224, 41559}, {226, 4311}, {238, 7609}, {284, 1108}, {371, 7968}, {372, 7969}, {376, 962}, {377, 12116}, {378, 1902}, {381, 5691}, {382, 1699}, {386, 37698}, {388, 6827}, {390, 12700}, {399, 33535}, {404, 3753}, {405, 5777}, {442, 24541}, {452, 24558}, {474, 11499}, {495, 6922}, {496, 950}, {497, 4305}, {498, 5252}, {499, 1837}, {500, 1064}, {501, 759}, {511, 1386}, {512, 44811}, {513, 35050}, {516, 550}, {519, 549}, {528, 49600}, {529, 21077}, {537, 51045}, {542, 32238}, {546, 3817}, {547, 19883}, {548, 4301}, {573, 1100}, {574, 31430}, {575, 4663}, {578, 44547}, {581, 995}, {590, 49601}, {595, 37469}, {601, 3915}, {602, 1468}, {612, 16434}, {614, 19544}, {615, 49602}, {632, 3634}, {692, 48694}, {726, 32448}, {730, 49111}, {758, 5428}, {760, 13335}, {891, 44805}, {912, 960}, {936, 5534}, {938, 6988}, {943, 1476}, {947, 1807}, {953, 1290}, {954, 51489}, {958, 997}, {971, 1001}, {978, 37699}, {991, 1279}, {1012, 9856}, {1055, 17451}, {1056, 4308}, {1058, 4313}, {1066, 4322}, {1072, 23675}, {1145, 38760}, {1149, 4300}, {1151, 31439}, {1152, 35774}, {1154, 12266}, {1160, 11371}, {1161, 11370}, {1191, 36746}, {1193, 5396}, {1203, 36750}, {1210, 15325}, {1317, 21154}, {1320, 34474}, {1329, 10942}, {1334, 17439}, {1350, 38315}, {1351, 16475}, {1353, 34379}, {1375, 25935}, {1376, 10156}, {1387, 4304}, {1389, 27003}, {1400, 17440}, {1426, 1870}, {1441, 17221}, {1455, 10571}, {1457, 4303}, {1478, 6928}, {1479, 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{3646, 9845}, {3647, 12104}, {3649, 30264}, {3651, 45977}, {3671, 24470}, {3679, 5054}, {3683, 5693}, {3720, 4192}, {3730, 6603}, {3742, 7686}, {3751, 5050}, {3754, 34353}, {3811, 12513}, {3812, 6796}, {3813, 32214}, {3820, 5795}, {3824, 6917}, {3827, 15577}, {3828, 11539}, {3830, 34628}, {3845, 12571}, {3851, 7988}, {3853, 28190}, {3868, 37106}, {3869, 3916}, {3871, 38460}, {3872, 4855}, {3874, 31806}, {3877, 4189}, {3878, 4640}, {3880, 8715}, {3890, 6950}, {3893, 48696}, {3911, 37728}, {3920, 19649}, {3928, 4930}, {3929, 28451}, {3955, 17625}, {3962, 4867}, {4004, 48363}, {4083, 39227}, {4084, 4973}, {4132, 39210}, {4145, 44812}, {4188, 35271}, {4190, 37000}, {4199, 24550}, {4220, 7191}, {4225, 18180}, {4251, 40133}, {4256, 4646}, {4276, 18178}, {4292, 39542}, {4294, 6948}, {4298, 6147}, {4302, 12701}, {4314, 15172}, {4315, 5719}, {4317, 10404}, {4357, 29287}, {4421, 10912}, {4423, 10157}, {4512, 17571}, {4564, 14887}, {4649, 37510}, {4652, 11682}, {4653, 8143}, {4666, 7580}, {4668, 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{6963, 11681}, {6965, 26127}, {6971, 7951}, {6978, 10588}, {6980, 7741}, {6982, 10591}, {6989, 19843}, {6992, 20076}, {6996, 16826}, {6998, 16823}, {6999, 29586}, {7171, 12705}, {7330, 16418}, {7354, 7491}, {7377, 17397}, {7384, 29592}, {7387, 11365}, {7411, 29817}, {7483, 24987}, {7506, 8185}, {7583, 8983}, {7584, 13971}, {7587, 12491}, {7588, 8100}, {7675, 42884}, {7680, 37356}, {7681, 37406}, {7690, 48740}, {7692, 48741}, {7701, 28453}, {7970, 34473}, {7972, 17663}, {7973, 10606}, {7974, 21157}, {7975, 21156}, {7976, 22712}, {7977, 9751}, {7978, 15055}, {7983, 21166}, {7984, 12778}, {8012, 48263}, {8021, 23204}, {8068, 18976}, {8077, 8099}, {8092, 8130}, {8109, 12488}, {8110, 12489}, {8129, 8351}, {8141, 28454}, {8225, 12490}, {8229, 26230}, {8236, 35514}, {8543, 18450}, {8572, 17054}, {8677, 44807}, {8703, 12512}, {8717, 9943}, {8731, 25941}, {8760, 11247}, {8907, 18732}, {8981, 13883}, {9041, 50983}, {9310, 16601}, {9317, 24774}, {9519, 51531}, {9540, 19066}, {9548, 9567}, {9549, 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{12908, 31791}, {13099, 38717}, {13178, 38224}, {13329, 49478}, {13334, 14839}, {13349, 44660}, {13350, 44659}, {13405, 37364}, {13532, 38776}, {13605, 32423}, {13630, 31728}, {13729, 17618}, {13747, 24982}, {13912, 35255}, {13935, 19065}, {13936, 13966}, {13975, 35256}, {14074, 38451}, {14269, 30308}, {14636, 48882}, {14666, 50926}, {14830, 50881}, {14891, 51077}, {14893, 50862}, {15017, 38755}, {15067, 31752}, {15071, 18515}, {15122, 47476}, {15170, 31777}, {15462, 32278}, {15489, 45955}, {15623, 16374}, {15677, 16116}, {15681, 50865}, {15683, 50819}, {15684, 50806}, {15686, 50815}, {15687, 50802}, {15690, 34638}, {15692, 50810}, {15693, 34718}, {15694, 19875}, {15698, 34631}, {15700, 50805}, {15702, 50818}, {15704, 28150}, {15707, 34747}, {15708, 31145}, {15711, 51107}, {15718, 50817}, {15721, 50804}, {15723, 50871}, {15733, 42842}, {15735, 38668}, {15759, 51104}, {15829, 31424}, {15842, 15843}, {16058, 23168}, {16113, 28460}, {16138, 28461}, {16139, 21161}, {16174, 22938}, {16239, 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{24581, 48381}, {25082, 41391}, {25406, 39898}, {25485, 46684}, {25498, 29109}, {25525, 45630}, {25681, 37713}, {26006, 30810}, {26140, 27006}, {26202, 31649}, {26367, 49378}, {26368, 49377}, {26369, 49038}, {26370, 49039}, {26498, 45718}, {26507, 45717}, {26516, 45719}, {26521, 45720}, {26626, 36698}, {26725, 37230}, {28083, 34461}, {28216, 44245}, {28228, 46853}, {28473, 48328}, {28537, 48344}, {28538, 50977}, {28609, 34740}, {28850, 48932}, {29057, 49482}, {29207, 50290}, {29309, 41430}, {29311, 48886}, {29331, 50023}, {29369, 33682}, {29570, 37416}, {29660, 36530}, {29814, 37400}, {31434, 37709}, {31443, 37512}, {31670, 38035}, {31671, 38036}, {31672, 38037}, {31747, 32424}, {31790, 32183}, {31811, 32046}, {31822, 37411}, {32049, 45701}, {32486, 46362}, {32515, 50775}, {32905, 33812}, {33668, 49113}, {34200, 50808}, {34380, 51196}, {34789, 38753}, {35404, 51080}, {35610, 35811}, {35611, 35810}, {36505, 36561}, {36745, 44414}, {36754, 39523}, {37246, 38396}, {37251, 44425}, {37298, 50843}, {37365, 43223}, {37425, 48903}, {37712, 46219}, {37732, 49997}, {37806, 45272}, {37829, 38762}, {38064, 47359}, {38081, 51069}, {38116, 49688}, {38118, 49529}, {38144, 47355}, {38764, 50903}, {39582, 44545}, {40091, 45219}, {40998, 50241}, {43118, 45714}, {43119, 45713}, {43151, 43179}, {44214, 47321}, {44220, 44661}, {44580, 51096}, {44903, 51075}, {45410, 45427}, {45411, 45426}, {47033, 49176}, {47333, 47593}, {48877, 50420}, {48883, 48907}, {48887, 50418}, {51114, 51117}, {51115, 51116}

▸ Functional Relations25 relations

  • X1385 = midpoint of Xi and Xj for these {i,j}: {1, 3}, {2, 3655}, {4, 18481}, {5, 34773}, {8, 37727}, {10, 5882}, {20, 12699}, {21, 33858}, {40, 1482}, {100, 12737}, {104, 6265}, {142, 43175}, {165, 10247}, {214, 11715}, {355, 944}, {376, 3656}, {381, 50811}, {399, 33535}, {500, 9840}, {549, 50824}, {550, 22791}, {942, 31786}, {946, 4297}, {960, 12675}, {991, 31394}, {999, 37611}, {1071, 5887}, {1483, 5690}, {1537, 38761}, {1657, 41869}, {1768, 48667}, {2975, 37733}, {3057, 37562}, {3058, 28458}, {3241, 3654}, {3244, 11362}, {3428, 37533}, {3534, 31162}, {3576, 10246}, {3579, 10222}, {3635, 43174}, {3811, 12513}, {3830, 34628}, {3874, 31806}, {3878, 5884}, {3928, 4930}, {4301, 31730}, {4677, 34748}, {5434, 28459}, {5441, 47032}, {5450, 40257}, {5453, 48930}, {5535, 35457}, {5697, 25413}, {5720, 30283}, {5731, 5886}, {5805, 43161}, {5881, 18526}, {6210, 48908}, {6261, 12114}, {6264, 12331}, {6326, 12773}, {6684, 13607}, {6767, 30503}, {6769, 8158}, {7354, 7491}, {7966, 40587}, {7967, 26446}, {7972, 19914}, {7982, 12702}, {7984, 12778}, {7987, 37624}, {7991, 8148}, {8666, 22836}, {8715, 22837}, {9943, 45776}, {9957, 31788}, {10265, 33337}, {10297, 47469}, {10543, 37401}, {10609, 37726}, {10698, 12515}, {10738, 12119}, {11014, 11849}, {11179, 47358}, {11496, 12520}, {11700, 11713}, {11709, 11720}, {11710, 11711}, {11712, 11714}, {11722, 12265}, {12248, 16128}, {12262, 40658}, {12680, 40263}, {12696, 35241}, {12738, 38669}, {12898, 13211}, {12908, 31791}, {13600, 31798}, {13624, 15178}, {13743, 16132}, {14110, 24474}, {14666, 50926}, {14830, 50881}, {15071, 40266}, {15122, 47476}, {15171, 31775}, {15681, 50865}, {16139, 34195}, {18446, 22758}, {18990, 31789}, {19907, 38602}, {22770, 37531}, {23156, 31825}, {24257, 32941}, {25485, 46684}, {26086, 26087}, {26286, 46920}, {28609, 34740}, {31663, 33179}, {31732, 31738}, {31787, 31792}, {31790, 32183}, {33281, 33862}, {34718, 51093}, {34789, 38753}, {37425, 48903}, {37474, 46475}, {39870, 49511}, {43151, 43179}, {45715, 45716}, {47333, 47593}, {48882, 48909}, {48883, 48907}, {48893, 48894}

  • X1385 = reflection of Xi in Xj for these {i,j}: {1, 15178}, {3, 13624}, {4, 9955}, {5, 1125}, {10, 140}, {40, 31663}, {65, 5885}, {355, 9956}, {549, 50828}, {942, 13373}, {946, 5901}, {960, 31838}, {1071, 26201}, {1482, 33179}, {1483, 13607}, {3576, 31662}, {3579, 3}, {3627, 18483}, {3647, 12104}, {4640, 7508}, {4663, 575}, {5690, 6684}, {5694, 960}, {5876, 31751}, {6917, 3824}, {10222, 1}, {10225, 23961}, {10263, 31757}, {10284, 9957}, {11230, 38028}, {11231, 10165}, {11278, 10222}, {11500, 40262}, {11567, 33657}, {11699, 11720}, {12261, 11735}, {12611, 11729}, {12619, 6713}, {13464, 3636}, {15686, 50815}, {15687, 50802}, {17502, 3576}, {18357, 3628}, {18480, 5}, {22791, 13464}, {22792, 12608}, {22793, 946}, {22798, 16617}, {22935, 214}, {22936, 21}, {22937, 5428}, {22938, 16174}, {23841, 11695}, {23961, 18857}, {24474, 6583}, {24475, 12005}, {26202, 31649}, {31673, 546}, {31728, 13630}, {31730, 548}, {31737, 10627}, {31788, 40296}, {31811, 32046}, {31828, 31937}, {33592, 11281}, {33697, 4}, {33899, 6705}, {34339, 9940}, {34638, 15690}, {34648, 5066}, {34862, 5450}, {35004, 34339}, {37562, 13145}, {37623, 26286}, {37727, 32900}, {38138, 10172}, {38140, 11230}, {38176, 11231}, {40660, 10282}, {41347, 36}, {48887, 50418}, {48926, 48893}, {50796, 547}, {50808, 34200}, {50821, 549}, {50862, 14893}, {51118, 40273}

  • X1385 = isogonal conjugate of X1389

  • X1385 = complement of X355

  • X1385 = anticomplement of X9956

  • X1385 = reflection of X1385 in the X1X3

  • X1385 = circumcircle-inverse of X22765

  • X1385 = complement of the isogonal conjugate of X3417

  • X1385 = X3417-complementary conjugate of X10

  • X1385 = Xi-Ceva conjugate of Xj for these (i,j): {27003, 16669}, {33637, 513}

  • X1385 = X1-isoconjugate of X1389

  • X1385 = Xi-Dao conjugate of Xj for these (i,j): {3, 1389}, {355, 1385}

  • X1385 = crosspoint of Xi and Xj for these (i,j): {1, 15446}, {59, 43345}

  • X1385 = crosssum of X1 and X5903

  • X1385 = barycentric product X75*X2317

  • X1385 = barycentric quotient Xi/Xj for these {i,j}: {6, 1389}, {2317, 1}

  • X1385 = {Xi,Xj}-harmonic conjugate of Xk for these (i,j,k): {1, 35, 3057}, {1, 36, 65}, {1, 40, 1482}, {1, 46, 2099}, {1, 55, 9957}, {1, 56, 942}, {1, 65, 50194}, {1, 165, 7982}, {1, 484, 11009}, {1, 999, 5045}, {1, 1319, 24928}, {1, 1388, 25405}, {1, 1420, 999}, {1, 1482, 33179}, {1, 2077, 23340}, {1, 2646, 24929}, {1, 3295, 31792}, {1, 3304, 5049}, {1, 3333, 15934}, {1, 3337, 5425}, {1, 3361, 11529}, {1, 3576, 3}, {1, 3579, 11278}, {1, 3601, 3295}, {1, 3612, 55}, {1, 3746, 5919}, {1, 5010, 5697}, {1, 5119, 2098}, {1, 5204, 50193}, {1, 5563, 354}, {1, 5697, 5048}, {1, 5903, 11011}, {1, 7280, 5903}, {1, 7982, 10247}, {1, 7987, 40}, {1, 7991, 16200}, {1, 8273, 31793}, {1, 10246, 15178}, {1, 10269, 34339}, {1, 10310, 13600}, {1, 10882, 10441}, {1, 11012, 24474}, {1, 13462, 3333}, {1, 13624, 3579}, {1, 15803, 3340}, {1, 15931, 14110}, {1, 16192, 11531}, {1, 16203, 13373}, {1, 18398, 44840}, {1, 21842, 1319}, {1, 22765, 6583}, {1, 22766, 50195}, {1, 22767, 50196}, {1, 26285, 10284}, {1, 30282, 1697}, {1, 30389, 3576}, {1, 31662, 31666}, {1, 32612, 35004}, {1, 35202, 7957}, {1, 35242, 8148}, {1, 37525, 2646}, {1, 37535, 5885}, {1, 37561, 37562}, {1, 37571, 37080}, {1, 37587, 18398}, {1, 37605, 37582}, {1, 37616, 35}, {1, 37617, 37592}, {1, 37618, 56}, {1, 37620, 35631}, {1, 40293, 13601}, {2, 355, 9956}, {2, 944, 355}, {3, 35, 26086}, {3, 40, 31663}, {3, 55, 26285}, {3, 56, 26286}, {3, 942, 37623}, {3, 999, 11249}, {3, 1482, 40}, {3, 3295, 11248}, {3, 3576, 13624}, {3, 5885, 41347}, {3, 6767, 10306}, {3, 7373, 22770}, {3, 10202, 37582}, {3, 10246, 1}, {3, 10247, 12702}, {3, 10267, 32613}, {3, 10269, 32612}, {3, 10306, 35238}, {3, 10679, 10310}, {3, 10680, 3428}, {3, 11849, 2077}, {3, 12000, 35448}, {3, 12702, 165}, {3, 13624, 17502}, {3, 15178, 10222}, {3, 15934, 5709}, {3, 16202, 55}, {3, 16203, 56}, {3, 18443, 9940}, {3, 22765, 11012}, {3, 22770, 35239}, {3, 24299, 24929}, {3, 24926, 11567}, {3, 24927, 24928}, {3, 32612, 23961}, {3, 32613, 33862}, {3, 34471, 46920}, {3, 35004, 10225}, {3, 37525, 26287}, {3, 37533, 31793}, {3, 37535, 36}, {3, 37612, 5122}, {3, 37615, 942}, {3, 37621, 35}, {3, 37624, 1482}, {3, 45923, 46623}, {3, 50317, 37536}, {4, 3616, 5886}, {4, 5731, 18481}, {4, 5886, 9955}, {5, 1125, 11230}, {5, 18480, 38140}, {5, 38028, 1125}, {8, 631, 26446}, {8, 7967, 37727}, {10, 140, 11231}, {10, 10165, 140}, {20, 3622, 5603}, {20, 5603, 12699}, {21, 18444, 1071}, {21, 21740, 5887}, {21, 30285, 9959}, {35, 36, 14792}, {35, 13145, 3579}, {35, 34486, 37621}, {35, 37561, 3}, {35, 37616, 37600}, {36, 65, 37582}, {36, 10902, 3}, {36, 24926, 1}, {36, 33657, 10222}, {40, 3338, 37532}, {40, 3576, 7987}, {40, 7987, 3}, {40, 31663, 3579}, {40, 37571, 33596}, {40, 37624, 33179}, {46, 2099, 50193}, {46, 5204, 5122}, {55, 56, 8071}, {55, 1388, 1}, {55, 40296, 3579}, {56, 2098, 17437}, {56, 31786, 37623}, {56, 34471, 1}, {56, 37615, 13373}, {56, 37618, 5126}, {65, 10202, 5885}, {65, 11567, 10222}, {65, 37605, 36}, {78, 956, 34790}, {100, 4861, 10914}, {104, 21740, 1071}, {104, 33858, 26201}, {145, 3523, 5657}, {165, 7982, 12702}, {214, 51111, 10}, {226, 4311, 18990}, {354, 14110, 24474}, {354, 24474, 6583}, {355, 3655, 944}, {371, 35762, 7968}, {372, 35763, 7969}, {376, 10595, 962}, {376, 38314, 3656}, {377, 12116, 37820}, {382, 18493, 1699}, {388, 6827, 10526}, {392, 1071, 5887}, {405, 18446, 5777}, {496, 950, 18527}, {497, 6850, 10525}, {549, 1483, 5690}, {549, 5690, 6684}, {550, 10283, 22791}, {551, 946, 5901}, {551, 4297, 946}, {602, 1468, 5398}, {631, 7967, 8}, {632, 37705, 38042}, {632, 38042, 3634}, {942, 5126, 56}, {942, 46920, 10222}, {946, 51118, 40273}, {950, 44675, 496}, {958, 997, 5044}, {960, 993, 31445}, {962, 10595, 3656}, {962, 38314, 10595}, {993, 30144, 960}, {1001, 12114, 3560}, {1125, 34773, 18480}, {1151, 35775, 31439}, {1151, 44636, 35775}, {1152, 44635, 35774}, {1155, 11011, 5903}, {1159, 37545, 3339}, {1319, 2646, 1}, {1319, 24299, 15178}, {1319, 26287, 10222}, {1319, 37080, 20323}, {1319, 37525, 24929}, {1381, 1382, 22765}, {1387, 15171, 12053}, {1388, 3576, 31788}, {1388, 3612, 9957}, {1420, 13384, 1}, {1420, 37611, 11249}, {1479, 11376, 7743}, {1482, 7987, 31663}, {1482, 10246, 37624}, {1482, 33179, 10222}, {1482, 37624, 1}, {1483, 50824, 13607}, {1490, 5436, 6913}, {1656, 18525, 5587}, {1697, 37526, 3359}, {1698, 5881, 5790}, {1699, 9624, 18493}, {1702, 9615, 6221}, {2077, 3746, 11849}, {2098, 5217, 5119}, {2099, 5204, 46}, {2478, 12115, 37821}, {2646, 13151, 13624}, {2646, 20323, 37080}, {2646, 21842, 24928}, {2646, 24927, 15178}, {2646, 37080, 37571}, {2975, 4511, 72}, {3057, 26087, 10222}, {3057, 37600, 35}, {3086, 3486, 5722}, {3207, 34522, 169}, {3241, 3524, 3654}, {3244, 10164, 11362}, {3295, 8726, 31787}, {3295, 37606, 3601}, {3303, 10310, 10679}, {3304, 3428, 10680}, {3304, 8273, 3428}, {3333, 15934, 50192}, {3340, 15803, 36279}, {3361, 11529, 5708}, {3428, 8273, 3}, {3487, 6987, 5812}, {3526, 5790, 1698}, {3526, 18526, 5790}, {3530, 11362, 31447}, {3560, 6261, 31937}, {3576, 10269, 18857}, {3576, 13384, 37611}, {3576, 13624, 31666}, {3576, 15178, 3579}, {3576, 18443, 10269}, {3576, 30392, 10246}, {3576, 34471, 31786}, {3576, 34486, 37600}, {3576, 37615, 26286}, {3576, 37624, 31663}, {3579, 17502, 3}, {3579, 31666, 17502}, {3585, 5443, 17605}, {3586, 50443, 9669}, {3601, 8726, 3}, {3616, 5731, 4}, {3616, 18481, 9955}, {3624, 5587, 1656}, {3627, 38034, 18483}, {3628, 18357, 10175}, {3636, 13464, 10283}, {3653, 3655, 2}, {3746, 11014, 23340}, {3816, 18242, 5}, {3817, 31673, 546}, {3872, 4855, 5687}, {3878, 5267, 4640}, {4256, 15955, 4646}, {4297, 5901, 22793}, {4304, 12053, 15171}, {4305, 11373, 31795}, {4308, 5703, 1056}, {4867, 6763, 3962}, {5010, 5697, 37568}, {5048, 37568, 5697}, {5122, 50193, 46}, {5126, 25405, 3660}, {5126, 31786, 26286}, {5219, 9613, 9654}, {5248, 5450, 6914}, {5396, 13731, 34466}, {5426, 16132, 13743}, {5432, 10944, 10039}, {5433, 10950, 1737}, {5438, 9623, 9709}, {5441, 16173, 4857}, {5443, 36975, 3585}, {5563, 11012, 22765}, {5563, 15931, 11012}, {5563, 34890, 36}, {5563, 35597, 10222}, {5690, 6684, 50821}, {5690, 50824, 1483}, {5691, 8227, 381}, {5691, 25055, 8227}, {5790, 18526, 5881}, {5795, 6700, 3820}, {5882, 10165, 10}, {5885, 10902, 3579}, {5885, 11567, 50194}, {5885, 33657, 1}, {5886, 18481, 4}, {5903, 7280, 1155}, {6198, 37305, 1872}, {6200, 35642, 49226}, {6264, 15015, 12331}, {6265, 33858, 21740}, {6396, 35641, 49227}, {6583, 15931, 3579}, {6713, 31659, 140}, {6767, 10306, 37622}, {6883, 37700, 5044}, {6893, 12667, 18516}, {6897, 10806, 3434}, {6914, 13369, 34862}, {6917, 48482, 18407}, {6947, 10805, 3436}, {7354, 15950, 12047}, {7587, 18454, 12491}, {7588, 18456, 8100}, {7677, 30284, 5728}, {7688, 35202, 3}, {7967, 37727, 32900}, {7984, 15035, 12778}, {7987, 10246, 33179}, {7987, 11531, 16192}, {7987, 33179, 3579}, {7987, 37571, 50371}, {7988, 18492, 3851}, {7991, 16200, 8148}, {8071, 31788, 37623}, {8071, 46920, 10284}, {8077, 18448, 8099}, {8227, 50811, 5691}, {8583, 30283, 9947}, {9583, 18992, 3311}, {9940, 10267, 3579}, {9940, 13624, 32612}, {9940, 40296, 18856}, {9943, 10179, 45776}, {9955, 18481, 33697}, {9957, 11227, 31788}, {9957, 18856, 35004}, {9957, 25405, 1}, {10106, 13411, 495}, {10175, 19862, 3628}, {10222, 17502, 3579}, {10222, 31666, 3}, {10246, 10902, 11567}, {10246, 13624, 10222}, {10246, 16203, 37615}, {10246, 30389, 13624}, {10246, 31662, 17502}, {10246, 31666, 11278}, {10246, 32612, 33281}, {10246, 37561, 26087}, {10246, 37618, 13373}, {10247, 12702, 7982}, {10267, 10269, 3}, {10267, 18443, 34339}, {10267, 32612, 33862}, {10269, 32613, 23961}, {10283, 22791, 13464}, {10389, 10857, 6244}, {10698, 38693, 12515}, {10943, 37438, 2886}, {11012, 15931, 3}, {11108, 35272, 8583}, {11227, 31788, 40296}, {11230, 18480, 5}, {11248, 31787, 3579}, {11500, 25524, 6911}, {11510, 22768, 8069}, {11531, 16192, 40}, {11567, 37605, 41347}, {11567, 41347, 11278}, {11707, 11708, 1386}, {12047, 21578, 7354}, {12119, 16173, 10738}, {12667, 26105, 6893}, {12675, 31838, 5694}, {12898, 15061, 13211}, {13145, 15178, 26087}, {13151, 24299, 3}, {13151, 26287, 31666}, {13373, 13624, 26286}, {13607, 50828, 6684}, {13624, 33179, 31663}, {13624, 33281, 10225}, {13624, 34339, 23961}, {14636, 48909, 48882}, {15178, 17502, 11278}, {15178, 18857, 35004}, {15178, 26287, 24929}, {15178, 30389, 31666}, {15178, 31662, 13624}, {15178, 31663, 33179}, {15178, 34339, 33281}, {15325, 37730, 1210}, {15694, 50798, 19875}, {15701, 34748, 38066}, {16200, 35242, 7991}, {17437, 46920, 23960}, {17502, 31666, 13624}, {18444, 21740, 33858}, {18446, 19861, 45770}, {18857, 32613, 17502}, {18857, 34339, 32612}, {18990, 37737, 226}, {19860, 35262, 474}, {19883, 50796, 547}, {20323, 33596, 33179}, {20323, 37080, 1}, {20323, 50371, 1482}, {21161, 34195, 16139}, {21842, 37525, 1}, {22758, 45770, 5777}, {22938, 38044, 16174}, {23961, 33281, 35004}, {23961, 33862, 3}, {24299, 24927, 10246}, {24914, 37740, 10573}, {24926, 37605, 50194}, {24928, 24929, 1}, {25055, 50811, 381}, {25405, 26285, 10222}, {25935, 35290, 1375}, {26086, 37562, 3579}, {26285, 31788, 3579}, {26286, 31786, 3579}, {26365, 26366, 3576}, {26446, 37727, 8}, {26487, 26492, 2}, {30144, 32153, 5694}, {30282, 37526, 3}, {30283, 35272, 5720}, {30389, 30392, 1}, {31393, 37560, 49163}, {31663, 37624, 10222}, {31792, 33574, 31787}, {31838, 32153, 31445}, {32612, 32613, 3}, {32613, 34339, 3579}, {33862, 34339, 10225}, {33862, 35004, 3579}, {34471, 37615, 15178}, {34471, 37618, 942}, {34486, 37561, 35}, {34556, 34557, 17502}, {34628, 38021, 3830}, {34628, 51110, 38021}, {34748, 38066, 4677}, {34773, 38028, 5}, {35238, 37622, 10306}, {37080, 37571, 24929}, {37080, 50371, 33596}, {37561, 37621, 26086}, {37562, 37600, 26086}, {37582, 50194, 65}, {38013, 38014, 24929}, {38053, 43161, 5805}, {38155, 51073, 31399}, {40273, 51118, 22793}, {45620, 45621, 55}, {48460, 48461, 18443}, {50821, 50824, 51087}, {50821, 50828, 51084}, {50821, 51084, 51088}, {50823, 50829, 50821}, {50823, 50833, 50829}, {50824, 50825, 50831}, {50824, 50828, 50821}, {50824, 50832, 50828}, {50824, 50833, 50823}, {50825, 50827, 50821}, {50825, 50831, 50827}, {50827, 50828, 51086}, {50827, 51086, 50825}, {50828, 50829, 50833}, {50828, 51085, 50824}, {50828, 51087, 51088}, {50831, 51086, 50821}, {50832, 51085, 50821}, {51084, 51087, 50821}

  • X1385 = {X1,X40}-harmonic conjugate of X1483

  • X1385 = X5-of-2nd circumperp-triangle

  • X1385 = X3-of-X1-Brocard-triangle

  • X1385 = X140-of-hexyl-triangle

  • X1385 = X26-of-incircle-circles-triangle

  • X1385 = X3-of-anti-Aquila-triangle

  • X1385 = endo-homothetic center of Ehrmann side-triangle and circumorthic triangle; the homothetic center is X5

  • X1385 = X546-of-excentral-triangle

Notes

Let Na = X5-of-BCX1, Nb = X5-of-CAX1, Nc = X5-of-ABX1. X1385 is the antigonal image of X5 wrt NaNbNc. Also, X1385 = X265-of-NaNbNc. (Randy Hutson, December 10, 2016)

Let MaMbMc be the medial triangle. X1385 is the radical center of the incircles of AMbMc, BMcMa, CMaMb. (Randy Hutson, December 10, 2016)