PART 1: | Introduction and Centers X(1) - X(1000) | PART 2: | Centers X(1001) - X(3000) | PART 3: | Centers X(3001) - X(5000) |
PART 4: | Centers X(5001) - X(7000) | PART 5: | Centers X(7001) - X(10000) | PART 6: | Centers X(10001) - X(12000) |
PART 7: | Centers X(12001) - X(14000) | PART 8: | Centers X(14001) - X(16000) | PART 9: | Centers X(16001) - X(18000) |
PART 10: | Centers X(18001) - X(20000) | PART 11: | Centers X(20001) - X(22000) | PART 12: | Centers X(22001) - X(24000) |
PART 13: | Centers X(24001) - X(26000) | PART 14: | Centers X(26001) - X(28000) | PART 15: | Centers X(28001) - X(30000) |
PART 16: | Centers X(30001) - X(32000) | PART 17: | Centers X(32001) - X(34000) | PART 18: | Centers X(34001) - X(36000) |
PART 19: | Centers X(36001) - X(38000) | PART 20: | Centers X(38001) - X(40000) | PART 21: | Centers X(40001) - X(42000) |
PART 22: | Centers X(42001) - X(44000) | PART 23: | Centers X(44001) - X(46000) | PART 24: | Centers X(46001) - X(48000) |
PART 25: | Centers X(48001) - X(50000) | PART 26: | Centers X(50001) - X(52000) | PART 27: | Centers X(52001) - X(54000) |
PART 28: | Centers X(54001) - X(56000) | PART 29: | Centers X(56001) - X(58000) | PART 30: | Centers X(58001) - X(60000) |
PART 31: | Centers X(60001) - X(62000) | PART 32: | Centers X(62001) - X(64000) | PART 33: | Centers X(64001) - X(66000) |
PART 34: | Centers X(66001) - X(68000) | PART 35: | Centers X(68001) - X(70000) | PART 36: | Centers X(70001) - X(72000) |
X(12001) lies on these lines: {1,3}, {5,10529}, {11,11929}, {30,10806}, {104,5734}, {140,10587}, {145,6911}, {381,10532}, {405,10283}, {474,5844}, {956,5901}, {1056,6842}, {1058,7491}, {1478,10949}, {1483,3149}, {1537,10941}, {1598,11401}, {1616,5398}, {1656,10527}, {3244,11499}, {3560,10595}, {3621,6946}, {3622,6883}, {3623,6905}, {3843,10742}, {4317,5840}, {5070,9711}, {5093,9026}, {5288,9624}, {5434,10525}, {5790,10916}, {6959,10530}, {6985,7967}, {7517,10835}, {9301,10879}, {9654,10957}, {9655,10738}, {9669,10959}, {10804,11842}, {10931,11916}, {10932,11917}, {11911,11915}, {11949,11957}, {11950,11958}
X(12001) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10680,3), (1,10966,3295), (3,10247,12000), (56,10679,3), (999,1482,3), (3304,3338,999), (10529,10597,5), (10532,10943,381)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25355.
X(12002) lies on these lines:
{4,52}, {51,1657}, {140,6688}, {511,3850}, {550,5462}, {1216,3851}, {1656,5447}, {3522,5892}, {3523,11465}, {3854,5891}, {3858,10263}, {5056,10625}, {5059,9730}, {5068,10170}, {10219,11592}, {10575,11002}
X(12002) =
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25355.
X(12003) lies on this line: {6000, 10295}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25358.
X(12004) lies on these lines:
{3,49} et al
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25365.
X(12005) lies on these lines: {1,104}, {3,3874}, {4,5557}, {5,2801}, {10,10202}, {12,10265}, {30,6583}, {40,3873}, {48,1729}, {57,6796}, {65,4311}, {72,10165}, {84,11020}, {140,3678}, {354,946}, {355,5883}, {515,942}, {517,548}, {518,5771}, {551,5887}, {581,982}, {631,5904}, {758,1385}, {912,1125}, {938,6256}, {944,4317}, {950,5570}, {952,3754}, {1006,6763}, {1064,3953}, {1210,10958}, {1482,3892}, {1483,2802}, {1490,10980}, {2771,5901}, {3149,4860}, {3218,10902}, {3333,6261}, {3336,11491}, {3337,6905}, {3555,11362}, {3576,3868}, {3577,9845}, {3616,5693}, {3651,5536}, {3742,5777}, {3833,9956}, {3878,10246}, {3889,7982}, {3894,7987}, {4015,11231}, {5045,6001}, {5253,6326}, {5439,10175}, {5542,6245}, {5708,11500}, {5728,6260}, {5770,10198}, {6705,11018}, {6952,11219}, {9948,10569}, {10573,10805}, {11025,11372}
X(12005) = midpoint of X(i) and X(j) for these {i,j}: {1,5884}, {3,3874}, {65,5882}, {3555,11362}, {11570,11715}
X(12005) = reflection of X(i) in X(j) for these (i,j): (3678,140), (3754,5885), (6684,9940)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25365.
X(12006) lies on these lines: {2,6102}, {3,143}, {5,113}, {30,5462}, {51,550}, {52,549}, {54,1511}, {140,389}, {156,6642}, {182,1658}, {186,6152}, {381,10574}, {382,5640}, {511,3530}, {546,5943}, {547,5907}, {548,5446}, {568,631}, {632,5562}, {1112,3520}, {1199,1493}, {1539,3521}, {1656,5876}, {1657,9781}, {1986,6143}, {3523,6243}, {3526,5889}, {3528,11002}, {3628,10219}, {3845,10575}, {3850,6000}, {3851,6241}, {3858,11381}, {5012,5944}, {5054,11412}, {5055,11465}, {5070,11459}, {6146,9827}, {7514,9786}, {7526,10601}, {9703,11423}, {10272,11806}, {11245,11264}
X(12006) = midpoint of X(i) and X(j) for these {i,j}: {3,143}, {52,10627}, {125,11561}, {140,389}, {548,5446}, {5462,9729}, {6102,11591}, {8254,11802}, {10272,11806}
X(12006) = reflection of X(i) in X(j) for these (i,j): (3628,11695), (10095,5462), (10627,11592)
X(12006) = complement of X(11591)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25365.
X(12007) lies on these lines: {3,3629}, {4,6}, {5,6329}, {20,5102}, {30,5097}, {69,10303}, {98,9300}, {125,11245}, {140,3631}, {141,3526}, {182,524}, {193,5085}, {511,548}, {542,5066}, {575,3564}, {578,6696}, {597,1352}, {1350,1992}, {1351,3534}, {2854,9826}, {3398,7789}, {3523,11008}, {3567,9973}, {3618,7486}, {3815,9755}, {3818,3857}, {5306,9744}, {6144,10519}, {6247,11426}, {6279,11314}, {6280,11313}, {6676,11225}, {10168,11540}, {10192,11433}, {11064,11422}
X(12007) = midpoint of X(i) and X(j) for these {i,j}: {3,3629}, {6,8550}, {182,1353}, {5480,6776}, {8584,11179}
X(12007) = reflection of X(i) in X(j) for these (i,j): (5,6329), (3589,575), (3631,140)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25373.
X(12008) lies on the cubic K040 and this line: {1,1030}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25379.
X(12009) lies on these lines: {1,3}, {3988,10124}, {5550,5694}
As a point on the Euler line, X(12010) has Shinagawa coefficients [3*E+40*F, -9*E+8*F].
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25379.
X(12010) lies on these lines: {2,3}, {11557,11591}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25380.
X(12011) lies on these lines: {186,1291}, {550,1263}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25381.
X(12012) lies on these lines: {2,10184}, {3,275}, {418,10003}, {549,1154}
X(12012) = reflection of X(10184) in X(2)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25381.
X(12013) lies on these lines: {547,11197}, {1656,3462}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25389.
X(12014) lies on these lines:
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25394.
X(12015) lies on this line: {7,2475}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25395.
X(12016) lies on these lines:
{1,104}, {7,151}, {56,11713}, {57,102}, {65,1359}, {117,226}, {124,1210}, {354,1361}, {518,3040}, {928,11028}, {942,2818}, {974,2779}, {1845,5902}, {2807,3664}, {3042,3812}, {3340,10696}, {3586,10732}, {3738,10015}, {3911,6711}, {4654,10709}, {5722,10747}, {9579,10726}
X(12016) = midpoint of X(65) and X(1364)
X(12016) = reflection of X(3042) in X(3812)
X(12016) = incircle-inverse-of-X(104)
X(12016) = X(131)-of-intouch-triangle
The Schoute circle is here defined as the radical circle of the Schoute coaxal system; that is, the circle with diameter X(15)X(16) and center X(187).
X(12017) lies on these lines:
X(12017) = reflection of X(1351) in X(11482)
X(12017) = Brocard-circle-inverse of X(33878)
X(12017) = Schoute-circle-inverse of X(5013)
X(12017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,182,5050), (3,5050,1351), (3,5093,1350), (6,5085,5092), (6,5092,3), (15,16,5013), (182,5085,3), (182,5092,6), (575,1350,5093), (1353,3530,10519), (5012,7484,3167), (5085,10541,182), (6200,8375,6221), (6221,6398,5024), (6396,8376,6398), (11485,11486,9605).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25401.
X(12018) lies on this line: {2475,2802}
See Tran Quang Hung and César Lozada, Hyacinthos 25418.
X(12019) lies on these lines: {1,5}, {2,10609}, {4,653}, {8,4767}, {10,528}, {30,1155}, {44,5179}, {46,3627}, {65,546}, {100,405}, {104,3149}, {140,10572}, {149,1145}, {153,6835}, {214,6667}, {381,1159}, {382,1788}, {429,1862}, {497,5790}, {515,5126}, {517,11545}, {519,5087}, {632,3612}, {938,9654}, {942,2801}, {950,9956}, {960,2802}, {1086,6788}, {1320,3621}, {1478,4860}, {1479,5690}, {1482,10591}, {1656,3486}, {1698,6174}, {1728,5128}, {1770,3853}, {1836,3845}, {1985,3240}, {2646,3628}, {2771,7687}, {2800,6797}, {2829,6245}, {3035,3634}, {3245,3583}, {3295,5818}, {3419,3820}, {3474,3830}, {3485,3851}, {3526,4305}, {3579,5840}, {3586,10993}, {3622,10031}, {3625,5854}, {3654,9580}, {3679,4679}, {3843,4295}, {4187,5086}, {4304,11231}, {4663,5848}, {4870,11737}, {4997,6790}, {5204,10090}, {5217,10058}, {5220,5856}, {5225,6928}, {5229,5708}, {5550,6224}, {5560,10483}, {5657,9668}, {5691,11219}, {5714,9803}, {5855,11813}, {6147,10895}, {6914,11502}, {9779,11041}, {10246,10589}, {10573,10896}, {11604,11684}
X(12019) = midpoint of X(i) and X(j) for these {i,j}: {11,80}, {149,1145}, {1317,9897}
X(12019) = reflection of X(i) in X(j) for these (i,j): (214,6667), (1387,11), (3035,6702), (9945,3035)
X(12019) = complement of X(10609)
X(12019) = Fuhrmann circle-inverse-of-X(5722)
X(12019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (355,9581,496), (1837,10826,5), (5587,5722,495), (7741,10950,5901)
See Angel Montesdeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio. See also X(8160) and X(12021).
X(12020) lies on these lines: {3,6}, {76,2546}, {1428,3238}, {1503,5403}, {1676,3934}, {2330,3237}, {3589,5404}
X(12020) = reflection of X(12021) in X(182)
X(12020) = {X(2030),X(3094)}-harmonic conjugate of X(12021)
X(12020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39,1343,8160), (1343,1671,39)
See Angel Montesdeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio. See also X(8160) and X(12020).
X(12021) lies on these lines: {3,6}, {76,2547}, {1428,3237}, {1503,5404}, {1677,3934}, {2330,3238}, {3589,5403}
X(12021) = reflection of X(12020) in X(182)
X(12021) = {X(2030),X(3094)}-harmonic conjugate of X(12020)
X(12021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39,1342,8161), (12020,12021,2030), (1342,1670,39)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25420 and Hyacinthos 25493 .
X(12022) lies on these lines:
{3,3580}, {4,6}, {5,49}, {30,568}, {51,7576}, {68,7503}, {125,11430}, {141,7550}, {184,403}, {185,1986}, {235,1614}, {378,1899}, {381,11402}, {389,6240}, {436,6761}, {468,11464}, {511,11660}, {539,5891}, {546,11423}, {550,3581}, {569,9927}, {578,1594}, {1593,11457}, {1885,6241}, {1994,3153}, {3448,7527}, {3542,9707}, {3564,11459}, {3567,3575}, {3628,11704}, {5446,11750}, {5562,5965}, {5876,11264}, {6193,6816}, {6756,9781}, {7507,11426}, {9545,9820}, {9818,11442}, {9833,10594}, {10018,10182}, {10127,11451}, {10282,10619}, {10295,11438}, {10297,11422}
X(12022) = reflection of X(i) in X(j) for these (i,j): (5890,11245), (7576,51)
X(12022) = X(5692)-of-orthic-triangle if ABC is acute
X(12022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,6776,11456), (265,567,5)
See X(7688) and Antreas Hatzipolakis and César Lozada, Hyacinthos 25420 and Hyacinthos 25493 . See also Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25511 .
X(12023) lies on the Jerabek hyperbola.
X(12023) = isogonal conjugate of X(13620)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25420 and Hyacinthos 25493 .
X(12024) lies on these lines: {4,6}, {30,11225}, {1899,11410}, {3628,5972}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25422.
X(12024) lies on this line: {1,5}
See Tran Quang Hung and César Lozada, Hyacinthos 25424.
X(12026) lies on these lines: {3,1263}, {5,49}, {30,137}, {128,3628}, {140,6592}, {549,930}
X(12026) = midpoint of X(i) and X(j) for these {i,j}: {3,1263}, {5,1141}
X(12026) = reflection of X(i) in X(j) for these (i,j): (128,3628), (6592,140)
The intriangle of a point given by trilinears x : y : z is the central triangle having A-vertex 0 : y + z cos A : z + y cos A. (See TCCT, p. 196). Thus, the A-vertex of the intriangle of X(6) is 0 : b + c cos A : c + b cos A. Contributed by César Lozada, February 11, 2017.
X(12027) lies on these lines: {3,5913}, {1296,9465}, {1995,5512}, {6776,7464}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25429.
X(12028) lies on these lines: {2, 5627}, {30, 50}, {94, 2071}, {186, 476}, {265, 2072}, {1141, 3153}
X(12028) = isogonal conjugate of X(1986)
See Tran Quang Hung and César Lozada, Hyacinthos 25436.
X(12029) lies on the circumncircle and these lines: {1,6079}, {100,1149}, {901,3915}, {995,2748} , {7292,9059}
See Tran Quang Hung and César Lozada, Hyacinthos 25436.
X(12030) lies on the circumncircle and these lines: {12,2222}, {21,1290}, {23,9070}, {28,2766}, {30,6011}, {74,6003}, {100,1325}, {101,4053}, {108,2074}, {109,5127}, {110,758}, {476,6757}, {523,759}, {842,7427}, {2651,4588}, {2691,4221}, {2701,4653}, {4227,10100}, {6012,7481}, {7469,9058}
X(12030) = trilinear pole of X(6)X(2610)
X(12030) = Λ(X(1), X(110))
See Tran Quang Hung and César Lozada, Hyacinthos 25436.
X(12031) lies on the circumncircle and these lines: {58,2702}, {98,6002}, {99,740}, {100,1931}, {101,1326}, {110,3747}, {511,6010}, {512,741}, {789,5209}, {813,1500}, {825,5006}, {2703,3736}
See Tran Quang Hung and César Lozada, Hyacinthos 25436.
X(12032) lies on the circumncircle and these lines: {1,927}, {3,813}, {41,919}, {100,2340}, {101,7193}, {103,9320}, {105,663}, {108,1429}, {109,2223}, {112,5009}, {741,7254}, {929,990}, {934,1458}, {991,1308}, {1305,3100}, {2222,5091}, {2704,11012}, {2737,5732}
X(12032) = reflection of X(813) in X(3)
X(12032) = circumcircle-antipode of X(813)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25437.
X(12033) lies on these lines: {55,2316}, {3196,6600}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25437.
X(12034) lies on these lines:
{3,3196}, {6,10247}, {9,48}, {44,517}, {45,10246}, {165,2246}, {952,4370}, {1635,2827}, {1743,2170}, {1766,3973}, {2291,2348}, {2792,10175}
X(12034) = midpoint of X(165) and X(9355)
X(12034) = X(3163)-of-excentral-triangle
For P on the circumcircle of a triangle ABC, let G(P) denote then centroid of the pedal triangle of P. The locus of G(P) is an ellipse, E, with center G = X(2), and the following pass-through points as shown here:
P | G(P) |
---|---|
X(74) | X(125) |
X(106) | X(3756) |
X(110) | X(5642) |
X(98) | X(6784) |
X(99) | X(6786) |
X(111) | X(6791) |
X(112) | X(6793) |
The ellipse E, described at X(6784), also passes through the vertices of the (pedal triangle of X(376)) = X(2)-of-antipedal-triangle-of-X(2), as well as the the following reflections:
X(5642) = reflection of X(125) in X(2)
X(6786) = reflection of X(6784) in X(2)
X(12035) = reflection of X(3756) in X(2)
X(12036) = reflection of X(6791) in X(2)
X(12037) = reflection of X(6793) in X(2)
See César Lozada, Hyacinthos 25463.
X(12035) lies on these lines:
{2,1280}, {121,519}, {524,5205}, {900,1635}, {952,10713}, {1086,9458}, {1213,6791}, {1647,4152}, {3679,5854}
X(12035) = midpoint of X(2) and X(3699)
X(12035) = reflection of X(3756) in X(2)
X(12035) = tripolar centroid of X(2415)
X(12035) = centroid of (degenerate) pedal triangle of X(1293)
See X(12035) and César Lozada, Hyacinthos 25463.
X(12036) lies on these lines:
{2,5503}, {125,599}, {126,524}, {351,690}, {538,9127}, {542,10717}, {543,5108}, {1992,4563}, {5477,8030}, {5650,6784}, {5969,9172}, {6786,9023}
X(12036) = midpoint of X(2) and X(9146)
X(12036) = reflection of X(6791) in X(2)
X(12036) = tripolar centroid of X(2418)
X(12036) = centroid of (degenerate) pedal triangle of X(1296)
See X(12035) and César Lozada, Hyacinthos 25463.
X(12037) lies on these lines:
{2,6793}, {122,125}, {127,525}, {599,5642}, {2777,10718}, {2871,3917}, {6054,10519}
X(12037) = reflection of X(6793) in X(2)
X(12037) = tripolar centroid of X(2419)
X(12037) = centroid of (degenerate) pedal triangle of X(1297)
See Antreas Hatzipolakis and Angel Montesdeoca, and César Lozada, Hyacinthos 25470 and Hyacinthos 25471 .
Let NANBNC be the reflection triangle of X(5). Let OA be the circumcenter of ANBNC, and define OB and OC cyclically. Triangle OAOBOC is orthologic to the orthic triangle at X(12038). (Randy Hutson, June 7, 2019)
X(12038) lies on these lines:
{2, 9927}, {3, 49}, {4, 11449}, {5, 1511}, {20, 5654}, {24, 5446}, {26, 11202}, {30, 5448}, {52, 186}, {54, 5504}, {68, 631}, {74, 9705}, {110, 3520}, {140, 5449}, {156, 6000}, {182, 8548}, {378, 10539}, {382, 1495}, {511, 1658}, {539, 549}, {541, 5894}, {550, 5944}, {567, 2931}, {569, 5892}, {578, 5462}, {1069, 5217}, {1152, 8909}, {1614, 2071}, {3043, 11562}, {3157, 5204}, {3523, 6193}, {3524, 11411}, {3530, 3564}, {3576, 9928}, {3855, 10546}, {5010, 6238}, {5646, 7393}, {5657, 9933}, {5663, 10226}, {5890, 9545}, {6146, 10257}, {6200, 10666}, {6241, 9544}, {6396, 10665}, {6418,8912}, {6642, 11425}, {6689, 7399}, {6699, 10116}, {7280, 7352}, {7488, 10625}, {7503, 10170}, {7506, 11424}, {7514, 9938}, {7526, 9306}, {7575, 10263}, {8546, 8681}, {9707, 11413}, {10020, 10182}, {10298, 11412}, {10540, 11381}, {10645, 10662}, {10646, 10661}
X(12038) = midpoint of X(i) and X(j) for these {i,j}: {3,1147}, {155,7689}, {156,11250}
X(12038) = reflection of X(i) in X(j) for these {i,j}: {5448,9820}, {5449,140}
X(12038) = complement of X(9927)
X(12038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,49,185), (3,155,7689), (3,1092,1216), (578,6644,5462), (1147,7689,155), (1614,2071,10575)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25471 .
X(12039) lies on these lines:
{6,373}, {39,9145}, {182,2393}, {193,7605}, {523,7804}, {524,547}, {575,2854}, {576,10170}, {597,5972}, {1843,2916}, {3618,5486}, {5092,8705}, {5650,10510}, {9730,11579}, {11003,11188}
X(12039) = midpoint of X(6) and X(8542)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25471 .
X(12040) lies on these lines:
{2,2418}, {3,9770}, {5,543}, {30,7618}, {39,9167}, {83,5503}, {99,3363}, {140,7610}, {182,524}, {538,7619}, {547,7615}, {550,7775}, {597,620}, {631,9740}, {1007,5077}, {2482,3815}, {2549,8355}, {3845,8176}, {3849,8703}, {5013,8360}, {5055,7620}, {5215,5306}, {7763,8359}, {7769,9166}, {7777,8598}, {7870,8362}, {8182,9766}, {8667,11812}
X(12040) = midpoint of X(i) and X(j) for these {i,j}: {2,11165}, {3,9770}, {7615,8716}, {7618,11184}, {8182,9766}
X(12040) = reflection of X(i) in X(j) for these (i,j): (5,9771), (549,7622), (3845,8176), (7610,140), (7615,547)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25471 . Also see Tran Quang Hung and Angel Montesdeoca, Hyacinthos 25680.
X(12041) lies on these lines:
{2,7728}, {3,74}, {5,1539}, {20,265}, {30,125}, {35,3028}, {55,10081}, {56,10065}, {64,9934}, {113,140}, {146,631}, {182,2781}, {185,10226}, {376,3448}, {378,1112}, {381,10721}, {511,11806}, {517,11709}, {541,549}, {542,8703}, {550,10264}, {567,1986}, {974,1204}, {1154,2071}, {1350,5621}, {1351,5622}, {1657,10733}, {2420,3269}, {2771,9943}, {2780,9208}, {2854,3098}, {2935,7526}, {3521,6143}, {3524,5655}, {3530,10272}, {3532,5504}, {3534,9140}, {3576,9904}, {3581,7464}, {3627,7687}, {3818,6698}, {5050,10752}, {5054,10706}, {5085,9970}, {5092,6593}, {5204,10091}, {5217,10088}, {5462,11807}, {5544,9818}, {6101,7689}, {6409,10819}, {6410,10820}, {6642,9919}, {6644,10117}, {6689,11805}, {7280,7727}, {7502,8717}, {7583,8994}, {7722,11003}, {7731,10574}, {7978,10246}, {8718,11559}, {9729,11557}, {10610,10628}, {11438,11746}
X(12041) = complement of X(7728)
X(12041) = circumcircle-inverse of X(10620)
X(12041) = X(11)-of-Trinh-triangle if ABC is acute
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25471 .
X(12042) lies on these lines:
{2,5191}, {3,76}, {5,2794}, {20,6321}, {30,115}, {32,2023}, {35,3027}, {36,3023}, {55,10069}, {56,10053}, {114,140}, {141,542}, {147,631}, {148,376}, {157,1605}, {182,10007}, {262,11842}, {378,5186}, {381,3972}, {404,5985}, {517,11710}, {543,8703}, {550,11623}, {632,6721}, {671,3534}, {1657,10723}, {1916,7793}, {2080,5999}, {2784,6684}, {3095,7766}, {3098,5969}, {3111,5663}, {3329,3398}, {3523,5984}, {3524,8289}, {3576,9860}, {3830,9166}, {3845,5461}, {4027,7824}, {5027,11176}, {5050,10753}, {5054,6054}, {5149,7815}, {5182,12017}, {5204,10089}, {5217,10086}, {5569,9830}, {5961,7502}, {5986,7485}, {5987,7496}, {6642,9861}, {6671,6771}, {6672,6774}, {7583,8980}, {7776,8781}, {7798,9737}, {7857,9873}, {7970,10246}, {8667,9888}, {8725,11606}, {9167,11812}, {10352,11285}
X(12042) = midpoint of X(i) and X(j) for these {i,j}: {3,98}, {20,6321}, {114,10991}, {376,11632}, {671,3534}, {1657,10723}, {1916,9821}, {2080,5999}, {6033,9862}, {6295,6582}, {8667,9888}, {8724,11177}, {8725,11606}
X(12042) = reflection of X(i) in X(j) for these (i,j): (5,6036), (114,140), (3845,5461), (5026,5092)
X(12042) = complement of X(6033)
X(12042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,9862,6033), (1078,5152,5976), (3524,11177,8724)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25476 .
X(12043) lies on these lines:
{2,3} et al
X(12043) = {X(140),X(2072)}-harmonic conjugate of X(3530)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25472 .
X(12044) lies on this line: {252,5449}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25490 .
X(12045) lies on these lines:
{2,51}, {575,6090}, {576,5544}, {3589,9027}, {3848,9026}, {5663,6723}, {6102,10170}, {8705,9822}
X(12045) = midpoint of X(i) and X(j) for these {i,j}: {3819,5640}, {5650,5943}
X(12045) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,10219,6688), (373,5650,11002), (373,11002,5943)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25490 .
X(12046) lies on these lines:
{2,11592}, {5,113}, {143,3090}, {156,11484}, {1216,10095}, {2979,9781}, {3567,11591}, {5447,10110}, {5876,11451}
X(12046) = midpoint of X(11017) and X(12006)
X(12046) = complement of X(11592)
X(12046) = {X(5),X(12006)}-harmonic conjugate of X(11017)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25491 .
X(12047) lies on these lines:
{1,4}, {2,46}, {3,1770}, {5,65}, {7,90}, {8,6871}, {10,908}, {11,113}, {12,517}, {19,5747}, {20,3612}, {21,36}, {30,2646}, {35,411}, {40,498}, {55,6985}, {56,3560}, {57,499}, {72,2886}, {80,7548}, {115,2653}, {124,1845}, {140,1155}, {142,3624}, {165,6988}, {191,5745}, {235,1905}, {238,1780}, {284,1839}, {354,496}, {355,2099}, {376,4333}, {377,997}, {381,1837}, {386,3914}, {431,1829}, {442,960}, {474,5880}, {484,6684}, {486,2362}, {495,3057}, {519,5086}, {527,6763}, {551,4311}, {553,1776}, {595,3011}, {631,3474}, {758,6734}, {938,6870}, {952,11011}, {962,3085}, {999,10404}, {1001,7742}, {1111,3674}, {1156,5557}, {1158,6833}, {1159,3851}, {1193,3120}, {1210,3671}, {1319,5901}, {1329,3753}, {1385,7354}, {1388,9657}, {1420,4317}, {1452,3542}, {1454,6862}, {1470,7702}, {1482,5252}, {1532,7686}, {1538,5806}, {1565,4059}, {1697,10056}, {1698,2093}, {1708,6832}, {1709,6847}, {1717,3100}, {1723,5746}, {1727,6888}, {1728,6846}, {1738,3216}, {1756,4357}, {1768,6705}, {1788,3090}, {1892,11399}, {1940,7551}, {2051,4424}, {2098,3656}, {2475,4511}, {2800,8068}, {3091,10826}, {3136,10974}, {3146,4305}, {3149,11507}, {3179,5243}, {3304,11373}, {3306,10200}, {3333,4654}, {3336,3911}, {3339,6855}, {3340,5587}, {3428,5812}, {3434,3811}, {3555,3813}, {3576,4299}, {3579,5432}, {3584,11010}, {3601,4302}, {3614,9956}, {3616,4293}, {3634,5445}, {3635,7972}, {3670,8229}, {3683,6675}, {3687,4647}, {3697,9710}, {3698,3820}, {3702,3936}, {3720,4303}, {3746,10624}, {3754,3814}, {3755,5312}, {3812,4187}, {3816,5439}, {3822,3878}, {3841,10176}, {3850,12019}, {3868,10916}, {3899,5837}, {3916,4999}, {3925,5044}, {3931,5718}, {3947,4301}, {4002,9711}, {4047,5742}, {4294,5703}, {4297,10483}, {4298,5563}, {4309,9580}, {4640,7483}, {4679,11108}, {4847,5904}, {4848,6874}, {4867,6737}, {5010,6876}, {5045,7743}, {5083,5533}, {5123,10107}, {5173,5777}, {5218,6361}, {5250,10198}, {5274,11036}, {5328,11024}, {5398,7299}, {5425,6738}, {5433,11230}, {5506,6666}, {5542,10394}, {5657,10588}, {5690,10592}, {5722,10896}, {5726,11531}, {5730,5794}, {5763,7957}, {5905,10527}, {6001,6831}, {6866,9581}, {6875,7280}, {6911,11509}, {6982,7982}, {6990,10395}, {7284,10586}, {7680,10523}, {7965,11018}, {8069,11496}, {9596,9620}, {9597,9619}, {9655,10246}, {10042,11372}, {10057,10698}, {10264,11670}, {10265,11571}, {10679,11501}, {10883,11019}
X(12047) = midpoint of X(1) and X(3585)
X(12047) = reflection of X(i) in X(j) for these (i,j): (3916,4999), (5267,1125), (10039,12)
X(12047) = X(49)-of-intouch-triangle
X(12047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,4,10572), (1,1699,1479), (1,3583,950), (1,5270,10106), (1,9612,1478), (4,3485,1), (4,3487,10393), (226,946,1), (497,3487,1), (1058,3475,1), (5290,11522,1)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio .
X(12048) lies on these lines: {3,6}, {237,8881}
X(12048) = {X(3),X(32)}-harmonic conjugate of X(12049)
X(12048) = {X(32),X(39)}-harmonic conjugate of X(1343)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio .
X(12049) lies on these lines: {3,6}, {237,8880}
X(12049) = {X(3),X(32)}-harmonic conjugate of X(12048)
X(12049) = {X(32),X(39)}-harmonic conjugate of X(1342)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio .
X(12050) lies on these lines:
{3,6}, {1501,8880}, {1676,3767}, {1677,2548}, {1701,9593}, {2546,5286}
X(12050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,182,12051), (6,1691,1343), (32,2035,1342), (182,12020,1343)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) and Circunferencias de Apolonio .
X(12051) lies on these lines: {3, 6}, {1501, 8881}, {1673, 16502}, {1676, 2548}, {1677, 3767}, {1700, 9593}, {2547, 5286}, {8880, 20965}
X(12051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): ): (6,182,12050), (6,1691,1342), (32,2036,1343), (182,12021,1342)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25498 .
X(12052) lies on these lines:
{30,9826}, {51,3258}, {476,1316}, {477,9781}, {523,11746}, {1112,3154}
X(12052) = midpoint of X(1112) and X(3154)
See Antreas Hatzipolakis and Angel Montedeoca, Hyacinthos 25502 .
The line AX(8) meets the incircle in two points, A' and A'', where A' is the point closer to A. Let σ be the affine transformation that carries A'B'C' onto A''B''C''. The finite fixed point of σ is X(12053). (Angel Montesdeoca, July 5, 2021)
X(12053) lies on these lines: {1, 4}, {2, 1697}, {3, 10624}, {5, 7743}, {7, 738}, {8, 3452}, {10, 11}, {12, 3817}, {20, 1420}, {21, 3254}, {30, 4311}, {35, 6940}, {40, 3086}, {46, 10072}, {55, 474}, {56, 516}, {57, 962}, {63, 10529}, {65, 4301}, {78, 5853}, {102, 1067}, {142, 390}, {145, 908}, {165, 7288}, {329, 6762}, {354, 3671}, {355, 9669}, {411, 2078}, {495, 9955}, {496, 517}, {498, 6983}, {499, 5119}, {518, 10392}, {519, 1837}, {527, 11240}, {550, 5126}, {551, 2646}, {553, 3333}, {595, 1936}, {758, 10959}, {936, 5082}, {938, 3340}, {960, 3813}, {993, 10966}, {999, 4292}, {1000, 5818}, {1071, 1537}, {1108, 8804}, {1155, 5493}, {1193, 3755}, {1201, 3914}, {1319, 4297}, {1329, 3880}, {1385, 1387}, {1388, 9670}, {1482, 5722}, {1616, 3772}, {1698, 9819}, {1737, 5697}, {1770, 5563}, {1776, 6763}, {1788, 7991}, {1836, 3304}, {1858, 3874}, {1864, 3555}, {1898, 2801}, {2066, 8983}, {2099, 6738}, {2136, 7080}, {2269, 5257}, {2321, 3702}, {2478, 3872}, {2550, 8583}, {2551, 4853}, {3023, 11599}, {3085, 6964}, {3091, 9578}, {3146, 4308}, {3243, 5809}, {3244, 5048}, {3295, 5886}, {3303, 11375}, {3306, 10586}, {3338, 4031}, {3361, 3474}, {3478, 10570}, {3501, 8568}, {3576, 4294}, {3577, 5804}, {3582, 11010}, {3600, 9579}, {3612, 4309}, {3622, 4313}, {3624, 5218}, {3649, 4890}, {3660, 9943}, {3663, 3665}, {3687, 4673}, {3741, 10480}, {3746, 6946}, {3753, 9843}, {3814, 10915}, {3816, 5836}, {3847, 5123}, {3877, 5837}, {3878, 10916}, {3885, 4193}, {3889, 10394}, {3895, 5552}, {3913, 6745}, {3953, 7004}, {4035, 4742}, {4310, 4907}, {4315, 7354}, {4425, 8240}, {4654, 11037}, {4668, 8275}, {4863, 6743}, {5045, 10391}, {5049, 6147}, {5068, 7320}, {5084, 9623}, {5086, 10707}, {5128, 5435}, {5250, 5745}, {5252, 10863}, {5261, 9779}, {5265, 9778}, {5281, 5550}, {5289, 6737}, {5433, 10164}, {5533, 10265}, {5536, 7098}, {5570, 5884}, {5587, 10591}, {5687, 6700}, {5703, 10389}, {5758, 10396}, {5768, 7971}, {5794, 11235}, {6705, 10785}, {6767, 11374}, {6796, 11508}, {6975, 7741}, {7988, 10588}, {8715, 11502}, {8808, 10373}, {9956, 10593}, {10043, 10051}, {10543, 11263}, {10580, 11518}
X(12053) = midpoint of X(i) and X(j) for these {i,j}: {1,1479}, {1837,2098}
X(12053) = reflection of X(i) in X(j) for these {i,j}: {10,3825}, {1210,496}, {4848,1210}, {5687,6700}, {6736,1329}
X(12053) = inner-Johnson-to-ABC similarity image of X(10)
X(12053) = Ursa-minor-to-Ursa-major similarity image of X(10)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) , where circles Oa, Ob, Oc are defined. Let A' be the point, other than A, in which the circles Ob and Oc intersect. Define B' and C' cyclically. Then X(12054) = X(3)-of-A'B'C'. (Peter Moses, February 25, 2017)
X(12054) lies on these lines:
{2,10131}, {3,6}, {5,7859}, {20,10359}, {30,83}, {36,10799}, {98,140}, {376,7787}, {378,11380}, {381,7808}, {382,10358}, {524,6308}, {538,8150}, {542,6292}, {549,1078}, {631,7836}, {1176,9407}, {1503,6287}, {2782,8290}, {3329,7470}, {3406,7709}, {3522,10788}, {3524,7793}, {3526,7915}, {4027,7824}, {4299,10797}, {4302,10798}, {5054,7815}, {5182,8359}, {5217,10801}, {5999,11272}, {6033,6656}, {6054,7944}, {6309,8177}, {7779,10357}, {7789,8724}, {7791,10349}, {7800,11179}, {7876,9996}, {7889,10168}, {8356,10350}, {9862,10333}
X(12054) = inverse-in-Brocard-circle of X(9821)
X(12054) = inverse-in-circle-{{X(1687),X(1688),PU(1),PU(2)}} of X(5007)
X(12054) = center of inverse-in-circle-{{X(1687),X(1688),PU(1),PU(2)}}-of-Moses-circle
X(12054) = harmonic center of Gallatly circle and circle {{X(1687),X(1688),PU(1),PU(2)}}
X(12054) = midpoint of centers of circles {{X(1379),PU(1)}} and {{X(1380),PU(1)}}
X(12054) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,6,9821), (3,182,3398), (3,3398,2080), (3,11842,5171), (20,10359,10796), (39,5092,3), (182,5092,1691), (1342,1343,5092), (1687,1688,5007), (5085,5116,5092)
See Angel Montedeoca, Hechos Geométricos en el Triángulo (2015) , where circles Oa, Ob, Oc are defined. Let A' be the point, other than A, in which the circles Ob and Oc intersect. Define B' and C' cyclically. Then X(12055) = X(6)-of-A'B'C'. (Peter Moses, February 25, 2017)
X(12055) lies on these lines:
{3,6}, {99,3589}, {141,7799}, {323,8041}, {732,7824}, {1495,10329}, {2023,8290}, {2502,7711}, {3231,5888}, {3619,7836}, {3763,7880}, {4048,7786}, {5103,7847}, {5254,7859}, {7757,8177}
X(12055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,5092,1691), (6,5116,5092), (39,5092,6), (39,5116,1691), (3094,5038,5111).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25504 .
See another construction: Antreas Hatzipolakis and Peter Moses, Euclid 102 .
X(12056) lies on this line: (2,3}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25504 .
X(12057) lies on this line: (2,3}
X(12057) = midpoint of X(140) and X(10289)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25506 .
X(12058) lies on these lines: {20,2979}, {22,1495}, {51,858}, {161,1350}, {185,1993}, {394,1619}, {511,1370}, {1216,11414}, {1843,7391}, {2071,5012}, {3060,7396}, {3819,7493}, {5447,9715}, {7667,9967}, {7998,10565}, {10625,11750}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25506 .
X(12059) lies on these lines: {63,3678}, {72,515}, {78,2801}, {144,3648}, {200,7992}, {329,1479}, {518,10392}, {758,3436}, {908,3825}, {1898,5853}, {2802,3632}, {2975,10176}, {3421,5693}, {3585,5176}, {3680,9951}, {3681,4882}, {3868,11678}, {3927,11499}, {4847,5777}, {5442,5744}, {5883,11681}, {6001,6736}, {6763,10090}
X(12059) = midpoint of X(1479) and X(5904)
X(12059) = reflection of X(3874) in X(3825)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25510 .
X(12060) lies on this line: {3,54}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25510 .
X(12061) lies on this lines:
{3,8705}, {5,11649}, {6,3518}, {52,2854}, {143,8584}, {156,576}, {235,1843}, {389,2393}, {511,3627}, {524,6243}, {575,5944}, {1192,8549}, {1503,6240}, {2781,11381}, {3517,11216}, {5449,8262}, {9019,10625}, {9781,9971}, {11188,11444}, {11441,11477}
X(12061) = midpoint of X(i) and X(j) for these {i,j}: {3,11663}, {6403,9973}
X(12061) = reflection of X(5480) in X(1843)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25510 .
X(12062) lies on these lines:
{3518,11935}, {3627,6243}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25510 .
X(12063) lies on these lines: {24,3431}, {7530,9716}
X-parabola and related centers: X(12064)-X(12079)
This preamble and centers X(12064)-X(12079) were contributed by César Eliud Lozada, February 27, 2017.
Let A*B*C* be the side triangle of the medial and orthic triangles of ABC, and let A'B'C' be the medial triangle of A*B*C*. Then A, B, C, A', B', C' lie on a parabola here named the X-parabola of ABC. Some properties of this parabola are:
Let ta, tb, tc be the tangents to the X-parabola at A, B, C, respectively; the triangle AtBtCt bounded by these tangents is here named the X-parabola-tangential triangle of ABC. Barycentric coordinates of A-vertex are:
At = -(b^2-c^2)^2 : (a^2-c^2)^2 : (a^2-b^2)^2
The appearance of (T,i) in the following list means that triangles T and X-parabola-tangential are perspective with perspector X(i): (ABC, 115), (extouch, 12069), (2nd Hatzipolakis, 12070), (incentral, 12071), (intouch, 12072), (Lemoine, 12073), (Macbeath, 12075), (medial, 523), (orthic, 512), (Steiner, 12076), (symmedial, 12077), (Yff contact, 12078).
The X-parabola is the isogonal conjugate of line X(110)X(351) (the tangent to circumcircle at X(110)), and the isotomic conjugate of line X(99)X(110) (the tangent to Steiner circumellipse at X(99)). (Randy Hutson, March 9, 2017)
The X-parabola-tangential triangle is the anticevian triangle of X(115). (Randy Hutson, June 27, 2018)
X(12064) lies on the curve Q077 and these lines: {110,8029}, {125,10278}, {523,5972}, {1112,2501}, {3448,5466}, {5663,10279}, {6723,10189}
X(12065) lies on these lines: {523,5972}, {3233,8029}
X(12066) is the trilinear pole of X(523)X(5972) which is the locus of radical centers of the circles centered at the vertices of ABC and tangent to lines through X(30) (i.e., parallel to Euler line). (Randy Hutson, March 9, 2017)
X(12066) lies on the Kiepert hyperbola and these lines: {98,10733}, {5466,12065}
X(12066) = Trilinear pole of the line {523,5972}
X(12067) = isogonal conjugate of {6,647}∩{3292,11063}
X(12067) = trilinear pole of the line {30,10279}
X(12068) lies on these lines: {2,3}, {125,3233}, {523,5972}, {5642,6070}, {11064,11657}
X(12068) = midpoint of X(i) and X(j) for these {i,j}: {125,3233}, {3154,7471}, {11064,11657}
X(12068) = complement of X(3154)
X(12068) = orthogonal projection of X(5972) on the Euler line
X(12068) = {X(2), X(7471)}-harmonic conjugate of X(3154)
X(12069) lies on these lines: {523,8045}, {4041,8029}, {4770,6367}
X(12070) lies on no lines {X(i), X(j)} for i, j ≤ 12069
X(12071) lies on these lines: {512,12069}, {523,8043}, {4041,4838}, {4705,8029}
X(12072) lies on these lines: {512,12069}, {523,2487}, {661,8029}
X(12072) = reflection of X(12069) in X(12071)
X(12073) lies on these lines: {30,511}, {83,5466}, {1637,3288}, {1649,3005}, {4108,9189}, {4808,4822}, {5027,9185}, {8371,11183}, {8723,9751}, {9123,9208}, {9180,11606}, {9485,9889}, {10183,10278}
X(12073) = crossdifference of every pair of points on line X(6)X(5888)
X(12073) = isogonal conjugate of X(12074)
X(12074) lies on the circumcircle and these lines: {39,111}, {98,549}, {662,2748}, {691,1634}, {827,5467}, {843,2076}, {2396,9069}, {9145,11636}
X(12074) = reflection of X(11638) in X(7711)
X(12074) = isogonal conjugate of X(12073)
X(12074) = trilinear pole of the line {6,5888}
X(12075) lies on these lines: {83,5466}, {460,512}, {523,4885}, {669,1637}, {826,850}, {2525,9148}, {3005,8029}, {6562,9209}
X(12075) = radical center of {nine-point circle, nine-point circle of medial triangle, orthosymmedial circle}
X(12076) lies on these lines: {115,8029}, {148,690}, {523,620}, {2079,7669}, {6036,10279}, {6721,8151}, {6722,10278}
X(12076) = reflection of X(i) in X(j) for these (i,j): (6036,10279), (8151,6721)
Let A'B'C' be the anticevian triangle of X(4). Let A"B"C" be the tangential triangle, wrt A'B'C', of the bianticevian conic of X(4) and X(6). The lines A'A", B'B", C'C" concur in X(12077). (Randy Hutson, March 9, 2017)
X(12077) lies on these lines: {6,2623}, {230,231}, {251,2395}, {648,9514}, {661,2171}, {826,3569}, {850,2525}, {1640,12073}, {2081,2600}, {3005,8029}, {3288,7927}, {5466,7608}
X(12077) = reflection of X(i) in X(j) for these (i,j): (647,2501), (2525,850), (3005,12075)
X(12077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (647,2501,1637), (3005,8029,12075)
X(12077) = intersection of trilinear polars of X(4) and X(5)
X(12077) = perspector of hyperbola {A,B,C,X(4),X(5)} (circumconic centered at X(137))
X(12077) = crossdifference of every pair of points on line X(3)X(54)
X(12077) = center of circumconic that is locus of trilinear poles of lines passing through X(137)
X(12077) = X(2)-Ceva conjugate of X(137)
X(12077) = polar conjugate of isotomic conjugate of X(6368)
X(12077) = X(63)-isoconjugate of X(933)
X(12077) = X(95)-isoconjugate of X(163)
X(12077) = perspector of ABC and orthocevian triangle of X(930)
X(12077) = barycentric product X(5)*X(523)
X(12077) = intersection of orthic axes of ABC and reflection triangle
X(12078) lies on these lines: {148,690}, {3120,8029}
Let MaMbMc = medial triangle. Let (𝒫a) be the parabola, tangent to Euler line, to NMa, and to the line BC at its vertex, so that its directrix, da, is parallel to BC. Define the lines db and dc cyclically. Let T be the triangle bounded by the lines da, db, dc. Then T is homothetic to ABC, and the center of homothety is X(12079). For a construction, see Paris Pamfilos, A Gallery of Conics by Five Elements, Forum Geometricorum 14 (2014) 295-348, paragraph 13.3, page 346: construct a conic tangent to the line at infinity, i.e. a parabola, tangent to three lines a, b, c and passing through [D], i.e. with given axis-direction. (Angel Montesdeoca, March 1, 2022)
X(12079) lies on the X-parabola, Gibert's cubics K217, K741, Gibert's curve Q078 and these lines: {2,9717}, {30,74}, {98,468}, {110,12068}, {115,2501}, {125,523}, {325,892}, {339,850}, {542,3233}, {868,2394}, {1503,11657}, {1552,10151}, {1648,2395}, {2452,5094}, {3448,7471}, {3470,3628}, {7473,9862}, {8749,8791}, {10257,10419}
X(12079) = midpoint of X(i) and X(j) for these {i,j}: {125,6070}, {3448,7471}
X(12079) = reflection of X(i) in X(j) for these (i,j): (110,12068), (3154,125)
X(12079) = reflection of X(476) in the axis of the X-parabola
X(12079) = vertex of inscribed parabola with focus X(74) (and perspector X(1494), axis X(30)X(74) and directrix X(4)X(523))
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25539.
X(12080) lies on these lines: {1109,1962}, {2650,3635}, {3957 ,6758}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25539.
X(12081) lies on these lines: {1,21}, {517,3724}, {523,663}, {740,4511}, {5844,10459}
As a point on the Euler line, X(12082) has Shinagawa coefficients (2*E+2*F, -5*E-2*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12082) lies on these lines: {2,3}, {159,5656}, {316,9723}, {511,11456}, {575,10984}, {576,7592}, {944,9911}, {1181,8718}, {1199,11482}, {1350,11459}, {1498,2781}, {1633,6361}, {3068,9695}, {3284,8743}, {3292,6759}, {4293,10833}, {4296,9645}, {8717,9730}, {10625,11441}
X(12082) = reflection of X(378) in X(22)
X(12082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,23,24), (3,1598,11284), (3,5198,3090), (3,7387,23), (3,7530,1995), (3,11284,631), (4,10323,7509), (4,11414,10323), (20,23,3), (20,7387,24), (26,1657,11413), (1995,7530,10594), (3146,7492,7527), (3529,7556,7464), (7464,7556,3), (7492,7527,3)
As a point on the Euler line, X(12083) has Shinagawa coefficients (3*E+4*F, -7*E-4*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12083) lies on these lines: {2,3}, {35,9658}, {36,9673}, {115,8553}, {159,399}, {161,6000}, {195,11577}, {265,5621}, {394,10540}, {567,3796}, {999,4351}, {1154,11456}, {1181,6243}, {1351,8547}, {1482,9911}, {2917,5895}, {3070,9683}, {3098,5891}, {3295,4354}, {3579,8185}, {3581,10605}, {5446,10984}, {5889,8718}, {6101,11441}, {6449,8276}, {6450,8277}, {6759,10625}, {7592,10263}, {7737,9609}, {8148,8192}, {9655,10831}, {9659,10483}, {9668,10832}, {9914,9920}, {10564,11202}, {10620,11820}
X(12083) = reflection of X(i) in X(j) for these (i,j): (3,22), (7391,5)
X(12083) = Stammler-circle-inverse-of-X(7574)
X(12083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,1598,1656), (3,3843,7395), (3,5073,1593), (3,5899,25), (3,7387,7517), (3,7517,7506), (3,9909,2070), (4,6636,7514), (20,26,3), (22,378,7502), (23,376,6644), (25,5899,7517), (378,7502,3), (1657,2937,3), (3146,7512,7526), (3627,7525,7503), (5198,7393,3851), (7387,11414,3), (7503,7525,3), (7512,7526,3), (7556,11001,2071)
As a point on the Euler line, X(12084) has Shinagawa coefficients (E-4*F, -3*E+4*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
Let La be the polar of X(3) wrt the A-power circle, and define Lb, Lc cyclically. Let A' = Lb∩Lc, B' = Lc∩La, C' = La∩Lb. Triangle A'B'C' is homothetic to ABC at X(5094) and to the anticomplementary triangle at X(22). X(4)-of-A'B'C' = X(1657), and X(5)-of-A'B'C' = X(12084). (Randy Hutson, March 9, 2017)
X(12084) lies on these lines: {2,3}, {49,11456}, {52,1204}, {56,8144}, {64,155}, {74,5889}, {143,9786}, {156,1498}, {184,10575}, {394,5876}, {511,7689}, {542,9925}, {1069,10060}, {1092,10564}, {1147,6000}, {1151,11265}, {1152,11266}, {1154,10606}, {1236,1975}, {1288,1294}, {2883,9820}, {3157,10076}, {3357,9938}, {3796,10610}, {4299,9672}, {4302,9659}, {4550,11793}, {5204,9645}, {5446,11438}, {5584,8141}, {5621,11255}, {5654,5878}, {5946,10982}, {6102,10605}, {6759,12038}, {7747,9608}, {7756,9609}, {9730,11424}, {10263,12041}, {10539,11381}, {11267,11480}, {11268,11481}, {11412,11440}
X(12084) = midpoint of X(64) and X(155)
X(12084) = reflection of X(i) in X(j) for these (i,j): (3,11250), (26,3), (1498,156), (1658,10226), (2883,9820), (6759,12038), (7387,1658), (11477,11255)
X(12084) = 1st-Droz-Farny-circle-inverse-of-X(403)
X(12084) = midpoint of X(3) and X(12085)
X(12084) = harmonic center of circumcircle and first Droz-Farny circle
X(12084) = harmonic center of tangential circle and Trinh circle
X(12084) = center of inverse-in-first-Droz-Farny-circle-of-nine-point-circle
X(12084) = reflection in X(5) of [center of inverse-in-second-Droz-Farny-circle-of-nine-point-circle]
X(12084) = center of circle that is the circumperp conjugate of the nine-point circle
X(12084) = circumperp conjugate of X(2072)
X(12084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,4,6644), (3,382,24), (3,1593,5), (3,1597,6642), (3,5073,2070), (3,7387,1658), (3,7395,549), (3,7503,7516), (3,7517,186), (3,7526,7514), (4,2071,3), (4,3548,5), (24,382,7530), (186,3146,7517), (1597,6642,546), (1658,7387,26), (1658,10226,3), (2041,2042,11799), (7503,7516,7514), (7516,7526,7503), (7529,11403,3845)
As a point on the Euler line, X(12085) has Shinagawa coefficients (E-2*F, -3*E+2*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12085) lies on these lines: {2,3}, {36,9645}, {52,10605}, {56,9629}, {68,6247}, {154,12038}, {155,6000}, {511,3357}, {999,8144}, {1069,6285}, {1092,11381}, {1147,1498}, {1181,10575}, {1350,9973}, {1351,6102}, {1619,5878}, {1853,9927}, {1993,6241}, {2777,9914}, {2883,5654}, {2935,9937}, {3157,7355}, {3260,3964}, {3527,5946}, {4299,10832}, {4302,10831}, {4550,5447}, {5446,9786}, {5907,11472}, {6001,9928}, {6221,11265}, {6238,10060}, {6398,11266}, {6800,8718}, {7352,10076}, {7689,10606}, {8778,10317}, {9730,10982}, {9908,9938}, {10539,10564}
X(12085) = reflection of X(i) in X(j) for these (i,j): (3,12084), (26,11250), (68,6247), (1498,1147), (7387,3), (9908,9938)
X(12085) = exsimilicenter of tangential circle and Trinh circle; the insimilicenter is X(3)
X(12085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,4,6642), (3,382,25), (3,1597,5), (3,1598,6644), (3,3830,7506), (3,5073,7517), (3,7517,3515), (3,9714,186), (3,9909,1658), (4,3546,5), (4,7464,11413), (4,11413,3), (22,3520,3), (26,11250,3), (376,7503,3), (550,7526,3), (2071,3146,24), (3522,7527,7509), (3627,6644,1598), (3830,7506,5198), (9715,11410,3)
As a point on the Euler line, X(12086) has Shinagawa coefficients (E-4*F, -4*E+4*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12086) lies on these lines: {2,3}, {52,74}, {54,10575}, {56,9539}, {64,1993}, {110,11381}, {185,1994}, {324,1105}, {511,11440}, {1204,3060}, {1498,9544}, {2935,3448}, {3357,5889}, {3580,6696}, {4550,7999}, {5584,9536}, {5866,7773}, {7355,9637}, {9306,11439}, {9545,11456}, {9786,11002}, {10539,11455}, {10574,11424}, {11003,11425}
X(12086) = reflection of X(7488) in X(3520)
X(12086) = 1st-Droz-Farny-circle-inverse-of-X(11563)
X(12086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,3146,23), (3,3627,3518), (3,11403,1995), (382,11250,186), (1593,11413,2)
As a point on the Euler line, X(12087) has Shinagawa coefficients (3*E+4*F, -8*E-4*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12087) lies on these lines: {2,3}, {52,8718}, {145,9911}, {161,6225}, {323,6759}, {3600,10833}, {7691,11381}, {8185,9778}
X(12087) = reflection of X(3520) in X(2937)
X(12087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20,7387,23), (26,3529,2071), (382,7512,7527), (2937,3520,7488), (5198,7485,5068)
As a point on the Euler line, X(12088) has Shinagawa coefficients (2*E+4*F, -5*E-4*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25532.
X(12088) lies on these lines: {2,3}, {110,10625}, {156,323}, {182,9781}, {185,8718}, {511,1614}, {515,9591}, {516,9626}, {575,1173}, {576,11423}, {1058,10833}, {1199,3060}, {1994,10263}, {2883,2917}, {2916,5480}, {2979,10539}, {3068,9683}, {3085,9658}, {3086,9673}, {3098,7999}, {3567,10984}, {3746,4354}, {4297,9625}, {4351,5563}, {5012,5446}, {5657,8185}, {6101,10540}, {6759,11412}, {7712,9545}, {7737,9700}, {8744,10316}, {9934,10628}
X(12088) = reflection of X(7488) in X(2937)
X(12088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,23,3518), (3,1995,3525), (3,3091,7550), (3,3627,7527), (3,3628,7496), (3,7530,3091), (3,7545,3628), (3,10594,3090), (4,22,7512), (20,26,186), (22,7387,4), (24,11414,376), (25,10323,631), (1598,7509,3545), (3091,7492,3), (3529,7556,3), (3547,7500,4), (3627,7555,3), (7485,7529,5067), (7492,7530,7550), (9909,11414,24)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25540.
Let ABC be a triangle with incenter X(1)=I and let a' be perpendicular line to AI through I. Denote as A'b the intersection of a' and the perpendicular line to AB through B and denote as A'c the intersection of a' and the perpendicular line through C to AC. Perpendicular lines to a' through A'b and A'c cut BC at Ab and Ac, respectively. Points Bc, Ba, Ca, Cb are built cyclically. Then these six points lie on a conic here named the Ashrafov-Montesdeoca conic. (See: Angel Montesdeoca, HGT-Feb 17, 2017).
An alternative construction of Ab and Ac: Let ABC be a triangle with incenter I=X(1) and let A'B'C' be the antipedal triangle of I (excentral triangle). The parallel lines to AI through C', B' cut BC at Ab and Ac, respectively. (Antreas Hatzipolakis, Hyacinthos 25529).
X(12089) lies on these lines: {65, 603}, {73, 2292}, {1071, 3931}, {1254, 1400}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25540.
Let ABC be a triangle, P = X(20) = De Longchamps point of ABC and let A'B'C' be the antipedal triangle of P. The parallel lines to AP through C', B' cut BC at Ab and Ac, respectively. Build Bc, Ba, Ca, Cb cyclically. Then these six points lie on a conic where named the Hatzipolakis-Montesdeoca-De Longchamps conic. (Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25540).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25543.
X(12091) lies on these lines: {3,476}, {30,1986}, {131,2072}, {523,7723}, {1368,11749}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25543.
X(12092) lies on the circumcircle and this line: {74,11250}
X(12092) = Ψ(X(4), X(49))
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25550.
X(12093) lies on these lines: {2,2854}, {114,325}, {183,9775}, {526,9185}, {1995,9145}, {2871,7998} , {5640,11163}, {5663,6054}, {5968,9155}, {9770,11002}, {9872,11580}, {10748,11185}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25550.
X(12094) lies on this line: {543,3629}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25553.
X(12095) lies on the cubic K038 and these lines: {2,5962}, {3,49}, {30,136}, {186,1299}
X(12095) = midpoint of X(186)) and X(10420)
X(12095) = complement of X(5962)
X(12095) = circumcircle-inverse-of-X(155)
X(12095) = inverse-in-complement-of-polar-circle of X(1216)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25553.
X(12096) lies on the cubic K038 and these lines: {3,64}, {30,122}, {131,10257}, {520,4091}, {631,6761}, {1304,2071}, {2060,3346}
X(12096) = midpoint of X(i) and X(j) for these {i,j}: {3,6760}, {1304,2071}
X(12096) = reflection of X(11589) in X(3)
X(12096) = complement of X(34170)
X(12096) = circumcircle-inverse-of-X(1498)
See Tran Quang Hung and César Lozada, Hyacinthos 25555.
X(12097) lies on these lines: {2, 17}, {6671, 8014}
See Tran Quang Hung and César Lozada, Hyacinthos 25555.
X(12098) lies on these lines: {2, 18}, {6672, 8015}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25559.
X(12099) lies on the Hutson centroidal ellipse and these lines: {4,10293}, {6,5505}, {25,5622}, {51,125}, {54,5643}, {74,1597}, {373,597}, {381,5640}, {526,1637}, {542,5943} et al.
X(12099) = midpoint of X(51) and X(125)
X(12099) = centroid of pedal triangle of X(125)
X(12099) = intersection of tangents to Walsmith rectangular hyperbola at X(6) and X(125)
As a point on the Euler line, X(12100) has Shinagawa coefficients: (11, -9).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25561.
Let A' be the circumcenter of BCX(2), and define B' and C' cyclically. The centroid of A'B'C'X(2) is X(12100). (Randy Hutson, March 9, 2017)
Let Oa be the circle centered at A with radius equal to the distance between X(2) and the midpoint of BC, and define Ob and Oc cyclically. X(12100) is the radical center of Oa, Ob, Oc. (Randy Hutson, March 9, 2017)
X(12100) lies on these lines:
{2,3}, {35,5298}, {36,4995}, {40,3653}, {165,3656}, {182,8584}, {187,9300}, {230,8589}, {395,10645}, {396,10646}, {524,5092}, {539,10213}, {541,10272}, {551,3579}, {553,5122}, {574,5306}, {597,3098}, {952,4669}, {1216,11592}, {1327,8253}, {1328,8252}, {1503,10193}, {1587,6497}, {1588,6496}, {1992,12017}, {2482,12042}, {3055,6781}, {3058,5010}, {3068,6452}, {3069,6451}, {3576,3654}, {3655,4677}, {3793,7837}, {3815,8588}, {3819,5663}, {4316,5326}, {4324,7294}, {4745,6684}, {5204,10056}, {5217,10072}, {5434,7280}, {5442,10543}, {5585,7737}, {5609,11693}, {5642,12041}, {6390,7771}, {6410,8981}, {6445,7586}, {6446,7585}, {6456,9540}, {7288,10386}, {7618,8667}, {7767,7799}, {7811,7871}, {8182,9766}, {9729,10627}, {9774,11149}, {10192,11204}
X(12100) =midpoint of X(i) and X(j) for these {i,j}: {2,8703}, {3,549}, {5,376}, {381,550}, {547,548}, {551,3579}, {597,3098}, {2482,12042}, {3534,3845}, {3655,5690}, {5642,12041}, {8182,12040}, {10192,11204}, {10304,11539}
X(12100) = reflection of X(i) in X(j) for these (i,j): (2,11812), (4,11737), (5,10124), (140,549), (381,3628), (546,547), (547,140), (549,3530), (3543,3861), (3830,3860), (3845,10109), (3853,381), (5066,2), (10109,11540)
X(12100) = complement of X(3845)
X(12100) = anticomplement of X(10109)
X(12100) = X(140)-Gibert-Moses centroid; see the preamble just before X(21153)
X(12100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,3,8703), (2,3830,5), (2,3845,10109), (2,5066,547), (3,381,10304), (5,3830,3860), (5,3860,5066), (140,3853,3628), (140,5066,2), (376,3839,1657), (381,631,11539), (381,5055,3544), (381,10304,550), (381,11539,3628), (3146,3523,631), (3146,10304,376), (3830,5054,2), (3845,8703,3534), (3845,10109,5066), (3853,11539,547), (3860,11812,10124), (5067,5073,3857)
As a point on the Euler line, X(12101) has Shinagawa coefficients: (1, -27).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25561.
X(12101) lies on these lines: {2,3}, {1327,6441}, {1328,6442}
X(12101) =midpoint of X(i) and X(j) for these {i,j}: {5,3543}, {381,3627}, {382,549}, {3830,3845}
X(12101) = reflection of X(i) in X(j) for these (i,j): (3,11737), (140,381), (376,3628), (381,3861), (547,546), (549,3850), (550,10124), (3534,11812), (5066,3845), (8703,10109), (10124,3856)
X(12101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,3845,3860), (4,3627,3861), (4,3830,3845), (4,3853,546), (4,5076,5), (5,3627,5073), (140,3853,3627), (140,3861,546), (381,5073,3524), (382,3839,549), (3146,3858,3530), (3524,3543,5073), (3534,3830,3543), (3534,5076,3830), (3543,3839,3522), (3543,3845,11812), (3627,3845,8703), (3627,3861,140), (3845,5066,546), (3856,11541,140), (5070,11541,550)
As a point on the Euler line, X(12102) has Shinagawa coefficients: (1, -19).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25561.
X(12102) lies on these lines: {2,3}, {517,4536}, {5447,11017}, {11565,11645}
X(12102) = midpoint of X(i) and X(j) for these {i,j}: {4,3853}, {140,382}, {546,3627}, {3543,5066}
X(12102) = reflection of X(i) in X(j) for these (i,j): (140,3856), (3530,3850), (3628,546), (3850,3861), (3861,4), (5447,11017), (11737,3845), (11812,381)
X(12102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,382,11541), (4,382,3845), (4,3543,3843), (4,3627,546), (4,3830,5), (4,5076,3627), (5,3627,3146), (382,3845,140), (382,5055,5059), (546,3853,3627), (3091,3146,376), (3091,11541,3), (3146,3523,3529), (3146,3525,1657), (3146,3830,3627), (3146,3839,3525), (3543,3843,550), (3627,5076,3853), (3628,3861,546), (3830,5054,3543), (3832,5073,549)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12103) lies on these lines: {2,3} et al
X(12103) =midpoint of X(20) and X(550)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12104) lies on these lines: {2,3} et al
X(12104) =midpoint of X(21) and X(5428)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12105) lies on these lines: {2,3} et al
X(12105) =midpoint of X(23) and X(7575)
X(12105) = {X(3),X(23)}-harmonic conjugate of X(37967)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12106) lies on these lines: {2,3} et al
X(12106) =midpoint of X(25) and X(6644)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12107) lies on these lines: {2,3} et al
X(12107) =midpoint of X(26) and X(1658)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 25562.
X(12108) lies on these lines: {2,3} et al
X(12108) =midpoint of X(140) and X(3530)
Let A'B'C' be the orthic triangle of a triangle ABC. Let Ia be the incircle of B'C'A, and define Ib and Ic cyclically. Let U be the smallest circle tangent to each of the three circles Ia, Ib, Ic. Then X(12109) = center of U. Let A'' be the touch point of U and Ia. Barycentrics are given by
A'' = -a (a+b-c) (a-b+c) (a^3 b^2-a b^4-2 a b^3 c-2 b^4 c+a^3 c^2-2 a b c^3-a c^4-2 b c^4) : b^2 (a+b-c) (a+c)^2 (-a+b+c) (-a^2+b^2+c^2) : (a+b)^2 (a-b-c) c^2 (a-b+c) (a^2-b^2-c^2) .
Contributed by Thanh Oai Dao and Peter Moses, March 4, 2017.
X(12109) lies on these lines: {1,181}, {4,150}, {10,9052}, {51,3868}, {72,5943}, {373,3876}, {511,942}, {517,6738}, {518,9822}, {576,3157}, {674,3812}, {912,10110}, {916,5806}, {938,5933}, {1046,3271}, {1722,3779}, {2810,3874}, {2841,4757}, {3690,5047}, {3819,5439}, {4662,9049}, {5044,6688}
Orthologic centers: X(12110)-X(12269)
Centers X(12210)-X(12269) were contributed by César Eliud Lozada, March 10, 2017.
The reciprocal orthologic center of these triangles is X(4).
X(12110) lies on these lines: {2,5171}, {3,83}, {4,32}, {5,316}, {6,11257}, {20,182}, {30,3398}, {39,11676}, {40,10791}, {51,401}, {55,10797}, {56,10798}, {99,3095}, {114,7785}, {194,576}, {211,11674}, {263,287}, {376,10359}, {381,10104}, {382,11842}, {384,511}, {385,6248}, {550,12054}, {631,7808}, {944,10800}, {946,11364}, {1003,10349}, {1351,1975}, {1478,10801}, {1479,10802}, {1513,7745}, {1614,3203}, {1632,9971}, {1656,7934}, {1691,5480}, {2782,7760}, {3090,7815}, {3091,7793}, {3098,10345}, {3146,9748}, {3552,9737}, {3575,6530}, {3818,9863}, {4027,6658}, {5034,7738}, {5039,6776}, {5097,7839}, {5188,7804}, {5476,7833}, {5691,10789}, {5870,10793}, {5871,10792}, {6054,7812}, {6284,10799}, {6785,10684}, {7608,11170}, {7709,7772}, {8541,11596}, {9821,10347}, {9838,11840}, {9939,11178}, {10795,11490}
X(12110) = X(4)-of-5th-anti-Brocard-triangle
X(12110) = 5th-anti-Brocard-to-ABC similarity image of X(4)
X(12110) = radical center of polar circles of ABC, 5th Brocard triangle, and 5th anti-Brocard triangle
X(12110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,10796,83), (4,32,98), (4,10788,32), (5,2080,1078), (20,7787,182), (5171,10358,2), (7737,9993,10722), (7808,8722,631)
The reciprocal orthologic center of these triangles is X(3).
X(12111) lies on these lines: {1,11446}, {2,185}, {3,74}, {4,52}, {5,5890}, {8,2807}, {15,11452}, {16,11453}, {20,2979}, {22,1498}, {30,11412}, {40,11445}, {51,3832}, {54,7526}, {64,394}, {69,6225}, {113,5449}, {143,3843}, {146,2888}, {155,378}, {186,7689}, {193,11469}, {235,3580}, {323,12086}, {343,2883}, {371,11447}, {372,11448}, {376,1216}, {381,3567}, {382,1154}, {389,3091}, {511,3146}, {546,568}, {567,11423}, {569,4550}, {576,11443}, {578,7527}, {631,5891}, {850,9242}, {858,6247}, {916,3868}, {930,6069}, {1092,2071}, {1147,3520}, {1181,5012}, {1204,9306}, {1351,11403}, {1593,1993}, {1594,7703}, {1657,6101}, {1658,10540}, {1870,6238}, {1885,3564}, {1994,11424}, {1995,9786}, {2060,5910}, {2779,5693}, {2781,5895}, {3090,9730}, {3100,6285}, {3101,6254}, {3167,3516}, {3193,4219}, {3522,3917}, {3523,11793}, {3525,10170}, {3528,5447}, {3529,10625}, {3534,10627}, {3545,5462}, {3574,5169}, {3627,6243}, {3830,10263}, {3839,10110}, {3851,5946}, {4296,7355}, {5055,11465}, {5067,5892}, {5068,5943}, {5422,11479}, {5448,7577}, {6198,7352}, {6696,7729}, {6759,7488}, {6895,10441}, {7486,11695}, {7592,9818}, {7728,7731}, {8549,11416}, {8718,8907}, {9545,11430}, {10282,10298}, {10546,11438}, {10675,11420}, {10676,11421}, {11220,11573}
X(12111) = reflection of X(i) in X(j) for these (i,j): (3,5876), (20,5562), (74,7723), (185,5907), (1657,6101), (3146,11381), (3529,10625), (5889,4), (6241,3), (6243,3627), (6293,2883), (7722,113), (7731,7728), (10575,1216)
X(12111) = anticomplement of X(185)
X(12111) = X(8)-of-1st-anti-circumperp-triangle if ABC is acute
X(12111) = X(4)-of-X(3)-Fuhrmann-triangle
X(12111) = pedal-isogonal conjugate of X(20)
X(12111) = X(20)-of-X(4)-anti-altimedial-triangle
X(12111) = X(20)-of-X(20)-anti-altimedial-triangle
X(12111) = X(20)-of-X(2)-adjunct-anti-altimedial-triangle
X(12111) = X(3)-of-X(4)-adjunct-anti-altimedial-triangle
X(12111) = homothetic center of Ehrmann side-triangle and 4th anti-Euler triangle
X(12111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,185,10574), (3,110,11449), (3,156,11464), (3,399,156), (3,5876,11459), (3,11440,11454), (3,11441,110), (3,11444,7998), (3,11459,11444), (3,11591,7999), (4,5889,3060), (110,11440,3), (185,5907,2), (3060,11439,4), (5876,6241,11444), (6241,11459,3), (7999,11459,11591), (7999,11591,11444), (11440,11441,11449), (11449,11454,3), (12276,12277,12272)
The reciprocal orthologic center of these triangles is X(74).
X(12112) lies on these lines: {3,7712}, {4,6}, {23,3581}, {30,146}, {74,186}, {110,841}, {156,12086}, {184,11455}, {352,1499}, {378,3426}, {394,11001}, {542,1533}, {1511,2071}, {1513,11580}, {1531,10706}, {1545,10658}, {1546,10657}, {1614,11381}, {1994,3830}, {2393,10752}, {3098,11459}, {3448,11799}, {3518,6241}, {3520,6759}, {3529,11441}, {3543,11004}, {5092,7550}, {5655,10989}, {5888,10170}, {5907,8718}, {6090,11820}, {6800,11472}, {7575,10620}, {7687,10821}, {7725,10814}, {7726,10815}, {7728,10296}, {7998,8717}, {8614,10308}, {9730,10545}, {12088,12111}
X(12112) = reflection of X(i) in X(j) for these (i,j): (74,1495), (323,399), (2071,10540), (3448,11799), (7464,110), (10296,7728), (10620,7575), (10989,5655)
X(12112) = {X(74), X(1495)}-harmonic conjugate of X(186)
X(12112) = X(74)-of-anti-orthocentroidal-triangle
X(12112) = 4th-Brocard-to-circumsymmedial similarity image of X(74)
The reciprocal orthologic center of these triangles is X(4).
X(12113) lies on these lines: {2,3}, {40,11900}, {55,11905}, {56,11906}, {944,11910}, {946,11831}, {1478,11912}, {1479,11913}, {2777,7740}, {3184,9033}, {5691,11852}, {5870,11902}, {5871,11901}, {6284,11909}, {9838,11907}, {9839,11908}, {9873,11885}, {11500,11848}, {11839,12110}
X(12113) = midpoint of X(20) and X(4240)
X(12113) = reflection of X(i) in X(j) for these (i,j): (4,402), (1650,3), (11897,11845)
X(12113) = X(4)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12114) lies on these lines: {1,84}, {3,10}, {4,11}, {5,6256}, {8,6909}, {12,6833}, {20,2894}, {21,3427}, {28,963}, {30,10525}, {36,3149}, {40,956}, {48,5776}, {55,944}, {57,7686}, {119,6958}, {153,6972}, {165,5258}, {219,1765}, {280,1295}, {281,1436}, {376,5584}, {381,10199}, {382,11928}, {388,6847}, {405,1490}, {474,5587}, {499,1532}, {513,945}, {516,8666}, {517,1158}, {518,3358}, {519,10306}, {550,11495}, {601,5710}, {946,999}, {952,3913}, {960,7330}, {971,1001}, {997,5777}, {1006,8273}, {1125,6260}, {1191,3073}, {1317,10965}, {1329,6891}, {1468,5706}, {1470,1837}, {1476,10309}, {1478,6831}, {1479,10948}, {1482,2800}, {1519,11376}, {1537,10052}, {1593,5101}, {1617,4311}, {1699,5563}, {1706,10270}, {2077,5687}, {2096,4295}, {2551,6926}, {2716,2765}, {2886,6850}, {2950,6264}, {3035,6961}, {3058,10806}, {3072,4252}, {3085,6935}, {3091,5253}, {3295,5882}, {3303,7967}, {3304,3649}, {3339,3577}, {3359,5836}, {3436,6890}, {3486,5768}, {3523,5260}, {3575,11390}, {3614,6879}, {3632,5537}, {3655,4428}, {3656,12001}, {3816,6893}, {3897,11220}, {3925,6897}, {4018,7982}, {4321,11372}, {4413,5818}, {4423,5658}, {4999,6825}, {5080,6943}, {5120,10445}, {5204,6905}, {5217,6950}, {5229,6844}, {5231,7580}, {5251,7987}, {5288,7991}, {5289,5887}, {5432,6977}, {5433,6834}, {5434,10532}, {5538,5904}, {5542,7373}, {5552,6966}, {5693,5730}, {5870,10920}, {5871,10919}, {5886,6259}, {6244,11362}, {6253,6934}, {6257,11371}, {6258,11370}, {6284,6938}, {6667,6981}, {6690,6892}, {6691,6944}, {6713,6959}, {6762,6769}, {6830,10895}, {6836,10522}, {6845,9657}, {6848,7288}, {6914,10267}, {6925,10527}, {6956,10590}, {6968,7173}, {6971,10742}, {7171,9943}, {7966,7990}, {8071,10572}, {9838,10945}, {9839,10946}, {9873,10871}, {9910,11365}, {10043,10058}, {10165,11108}, {10609,11517}, {10794,12110}, {10950,11509}, {11903,12113}
X(12114) = midpoint of X(i) and X(j) for these {i,j}: {1,84}, {1490,10864}, {2950,6264}, {5882,9948}, {6762,6769}, {7971,7992}
X(12114) = reflection of X(i) in X(j) for these (i,j): (3,5450), (10,6705), (3913,11248), (6256,5), (6260,1125), (6261,1385), (10525,10943), (11500,3)
X(12114) = X(4)-of-inner-Johnson-triangle
X(12114) = inverse-in-Feuerbach-hyperbola of X(56)
X(12114) = Ursa-minor-to-Ursa-major similarity image of X(4)
X(12114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1012,11496), (1,7992,7971), (3,355,1376), (3,9708,6684), (4,11,10893), (4,104,56), (4,3086,7681), (4,10785,11), (8,6909,10310), (20,2975,3428), (20,3434,11826), (36,5691,3149), (84,7971,7992), (944,6906,55), (993,4297,3), (1385,3560,1001), (1478,6831,10894), (2077,5881,5687), (3576,10864,1490), (10525,10943,11235)
The reciprocal orthologic center of these triangles is X(4).
X(12115) lies on these lines: {1,4}, {2,104}, {3,3436}, {5,10584}, {8,912}, {10,6897}, {11,6968}, {12,6833}, {30,10679}, {36,6880}, {40,10915}, {55,2829}, {56,6834}, {57,1512}, {63,2096}, {84,9578}, {100,6948}, {355,377}, {376,535}, {382,12000}, {390,10728}, {443,5818}, {495,1012}, {496,10598}, {498,5450}, {517,5905}, {529,3428}, {631,993}, {952,3434}, {956,6907}, {958,6889}, {999,1532}, {1001,6976}, {1125,6898}, {1158,10039}, {1181,9370}, {1317,10947}, {1329,6967}, {1376,6955}, {1385,2478}, {1389,5555}, {1470,4293}, {1621,6930}, {1837,11047}, {2550,2801}, {2975,6825}, {3085,6906}, {3086,6941}, {3090,3822}, {3091,10586}, {3304,7681}, {3575,11400}, {3576,6947}, {3577,4654}, {3600,6848}, {3616,6893}, {3913,11826}, {4190,11499}, {4297,6899}, {4299,6796}, {5080,5731}, {5193,6969}, {5218,6950}, {5251,6878}, {5252,6001}, {5253,6944}, {5260,6989}, {5261,6847}, {5437,5587}, {5768,6826}, {5804,11037}, {5870,10930}, {5871,10929}, {5884,10573}, {5886,6957}, {6259,10935}, {6284,10965}, {6830,10590}, {6831,9654}, {6836,10526}, {6838,10530}, {6842,10527}, {6862,10585}, {6872,10267}, {6879,7951}, {6891,11681}, {6929,10246}, {6934,7354}, {6935,8164}, {6949,7288}, {6952,10588}, {6982,11680}, {7680,11237}, {7686,10404}, {7966,9580}, {7992,10970}, {9838,11955}, {9839,11956}, {9873,10878}, {10085,10827}, {10803,12110}, {11914,12113}
X(12115) = reflection of X(i) in X(j) for these (i,j): (4,1478), (956,6907), (1012,495), (3434,6923), (6938,55)
X(12115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,4,10531), (1,1519,5603), (1,6256,4), (3,10942,5552), (4,388,10532), (4,1056,5603), (4,7967,497), (4,10597,946), (4,10805,1), (4,10806,1479), (119,10269,2), (498,5450,6977), (1479,5882,10806), (3359,6735,5657), (3421,6916,5657), (5080,5731,6827), (6831,9654,10599), (7354,10955,11509), (7354,11500,6934), (10246,10742,6929)
The reciprocal orthologic center of these triangles is X(4).
X(12116) lies on these lines: {1,4}, {2,10267}, {3,3434}, {5,10585}, {8,6827}, {10,6947}, {11,6834}, {20,104}, {30,10680}, {35,6977}, {40,6899}, {55,6833}, {56,5842}, {84,9580}, {100,6891}, {119,5187}, {145,6840}, {355,392}, {376,11012}, {377,1385}, {382,12001}, {390,6847}, {411,6585}, {495,10599}, {496,3149}, {498,6879}, {499,6796}, {517,6836}, {528,10310}, {631,2550}, {908,5534}, {912,11415}, {952,3436}, {958,6936}, {962,5768}, {1001,6832}, {1125,6854}, {1191,5721}, {1376,6967}, {1512,9581}, {1532,9669}, {1621,6824}, {1836,11048}, {2078,6927}, {2551,6902}, {2802,6903}, {2886,6889}, {2975,6868}, {3058,11496}, {3072,11269}, {3085,6830}, {3086,6905}, {3090,3825}, {3091,10587}, {3254,10305}, {3295,6831}, {3303,7680}, {3421,3984}, {3428,3813}, {3555,5812}, {3575,11401}, {3576,6897}, {3616,6826}, {3622,6839}, {3816,6983}, {3871,6943}, {4190,10269}, {4294,6906}, {4302,5450}, {5082,5657}, {5084,5818}, {5218,6952}, {5231,10268}, {5253,6885}, {5274,6848}, {5284,6887}, {5552,6882}, {5587,6898}, {5687,6922}, {5709,6361}, {5731,6850}, {5759,6601}, {5787,10936}, {5870,10932}, {5871,10931}, {5886,6835}, {6245,10624}, {6284,6938}, {6825,11680}, {6890,10530}, {6896,8227}, {6917,10246}, {6925,10525}, {6941,10591}, {6942,7288}, {6949,10589}, {6959,10584}, {6968,10896}, {7681,11238}, {7966,9578}, {7992,10971}, {9838,11957}, {9839,11958}, {9873,10879}, {10804,12110}, {10944,10953}, {11915,12113}
X(12116) = reflection of X(i) in X(j) for these (i,j): (4,1479), (3149,496), (3436,6928), (5687,6922), (6934,56)
X(12116) = anticomplement of X(11499)
X(12116) = X(4)-of-outer-Yff-tangents-triangle
X(12116) = inner-Yff-to-outer-Yff similarity image of X(4)
X(12116) = 1st-Johnson-Yff-to-2nd-Johnson-Yff similarity image of X(4)
X(12116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,4,10532), (3,10943,10527), (4,497,10531), (4,944,12115), (4,1058,5603), (4,7967,388), (4,10596,946), (4,10805,1478), (4,10806,1), (20,10529,11249), (499,6796,6880), (1478,5882,10805), (1532,9669,10598), (3583,6256,4), (5082,6865,5657), (6284,10949,10966), (6284,12114,6938)
The reciprocal orthologic center of these triangles is X(9855).
X(12117) lies on these lines: {2,9734}, {3,671}, {4,2482}, {20,542}, {30,99}, {35,10054}, {36,10070}, {98,376}, {114,3543}, {115,3524}, {148,6055}, {165,9875}, {262,11159}, {381,10723}, {511,8593}, {515,9881}, {517,9884}, {530,5474}, {531,5473}, {549,6321}, {620,3545}, {631,5461}, {1350,9830}, {1632,5648}, {2782,3534}, {2794,11001}, {2796,4297}, {2936,12082}, {3098,9878}, {3522,8596}, {3528,11623}, {3655,7983}, {4558,9214}, {5071,9167}, {5182,12110}, {5503,9744}, {5969,11257}, {7417,10717}, {8703,11632}, {8787,11477}, {9876,11414}, {9882,11824}, {9883,11825}, {10754,11179}
X(12117) = midpoint of X(20) and X(8591)
X(12117) = reflection of X(i) in X(j) for these (i,j): (4,2482), (98,376), (148,6055), (671,3), (3543,114), (6054,99), (6321,549), (7983,3655), (8591,10992), (10722,6054), (10723,381), (10754,11179), (11477,8787), (11632,8703)
X(12117) = anticomplement of X(9880)
X(12117) = orthologic center of these triangles: ABC-X3 reflections to McCay.
X(12117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (148,10304,6055), (549,6321,9166)
The reciprocal orthologic center of these triangles is X(9833).
X(12118) lies on these lines: {2,9927}, {3,68}, {4,110}, {5,11425}, {20,6193}, {30,155}, {35,10055}, {36,10071}, {165,9896}, {265,6640}, {376,539}, {381,9820}, {382,3167}, {515,9928}, {517,9933}, {542,3357}, {550,1350}, {569,6815}, {631,5449}, {912,3962}, {1060,9931}, {1069,6284}, {1181,4846}, {1216,11821}, {1352,7526}, {1370,11750}, {1503,12085}, {1657,11820}, {1993,6240}, {2071,11457}, {2929,2931}, {3070,8909}, {3098,9923}, {3157,7354}, {3520,11442}, {4299,7352}, {4302,6238}, {4549,5562}, {5446,7487}, {6560,10665}, {6561,10666}, {7505,11449}, {7528,11424}, {8548,11179}, {9908,11414}, {9929,11824}, {9930,11825}, {10112,11438}, {10619,10984}
X(12118) = midpoint of X(20) and X(6193)
X(12118) = reflection of X(i) in X(j) for these (i,j): (4,1147), (68,3), (9927,12038), (9936,6193), (11411,7689)
X(12118) = anticomplement of X(9927)
X(12118) = orthologic center of these triangles: ABC-X3 reflections to 2nd Hyacinth.
X(12118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,1147,5654), (376,11411,7689), (9927,12038,2)
The reciprocal orthologic center of these triangles is X(3).
X(12119) lies on these lines: {1,5840}, {3,80}, {4,214}, {11,3576}, {20,2800}, {30,6265}, {35,10057}, {36,10073}, {40,550}, {100,515}, {104,3651}, {119,5691}, {149,5731}, {165,9897}, {516,10698}, {517,4316}, {528,5732}, {631,6702}, {944,2802}, {946,10724}, {1145,5881}, {1317,7982}, {1320,5882}, {1385,4857}, {1490,2829}, {1699,11729}, {2801,5759}, {2932,11500}, {3035,5587}, {3612,8068}, {4293,5083}, {4299,11570}, {4996,5450}, {5444,6980}, {5531,6282}, {5660,10742}, {6262,11825}, {6263,11824}, {6713,7987}, {6869,9946}, {8988,9540}, {9613,10956}, {9912,11414}, {10058,10902}, {10090,10572}, {10768,11711}, {10769,11710}, {10770,11714}, {10771,11700}, {10772,11712}, {10777,11713}, {10778,11709}, {11014,11826}
X(12119) = midpoint of X(20) and X(6224)
X(12119) = reflection of X(i) in X(j) for these (i,j): (4,214), (80,3), (104,4297), (149,11715), (1320,5882), (5541,10993), (5691,119), (5881,1145), (6326,10609), (7982,1317), (10724,946), (10738,1385), (10768,11711), (10769,11710), (10770,11714), (10771,11700), (10772,11712), (10777,11713), (10778,11709)
X(12119) = anticomplement of X(6246)
X(12119) = {X(149), X(5731)}-harmonic conjugate of X(11715)
The reciprocal orthologic center of these triangles is X(40).
X(12120) lies on these lines: {1,5759}, {3,7091}, {35,10059}, {36,10075}, {40,3555}, {165,9898}, {517,8000}, {944,11519}, {956,10864}, {1490,3428}, {4326,6766}, {5584,9850}, {5732,6762}, {8726,11037}
X(12120) = midpoint of X(20) and X(9874)
X(12120) = reflection of X(7160) in X(3)
The reciprocal orthologic center of these triangles is X(6102).
Let La, Lb, Lc be the lines through A, B, C, resp. parallel to the Euler line. Let Ma, Mb, Mc be the reflections of BC, CA, AB in La, Lb, Lc, resp. Let A' = Mb∩Mc, and define B' and C' cyclically. Triangle A'B'C' is inversely similar to, and 3 times the size of, ABC. Let A"B"C" be the reflection of A'B'C' in the Euler line. The triangle A"B"C" is homothetic to ABC, with center of homothety X(125) and circumcenter X(12121). (See Hyacinthos #16741/16782, Sep 2008.) (Randy Hutson, July 21, 2017)
X(12121) lies on these lines: {74,550}, {113,382}, {146,3529}, {376,3448}, {381,5972}, {399,1498}, {511,11562}, {541,11820}, {542,1350}, {548,10264}, {549,11801}, {1154,7722}, {1539,3146}, {1656,7687}, {1986,6243}, {2771,12119}, {3028,4299}, {3070,10819}, {3071,10820}, {3520,6288}, {3581,10295}, {3627,10272}, {3830,5642}, {4324,7727}, {4549,7723}, {5054,6723}, {5648,11645}, {6146,10816}, {6240,11597}, {6284,10091}, {6449,8994}, {6759,11744}, {7354,10088}, {7574,10564}, {8703,9140}, {9143,11001}, {9730,11800}, {10117,12083}, {10263,11561}, {10625,10628}
X(12121) = midpoint of X(i) and X(j) for these {i,j}: {146,3529}, {399,1657}, {9143,11001}
X(12121) = reflection of X(i) in X(j) for these (i,j): (4,1511), (67,3098), (74,550), (146,5609), (265,3), (382,113), (3146,1539), (3448,12041), (3581,10295), (3627,10272), (3830,5642), (6243,1986), (7574,10564), (7728,110), (9140,8703), (10263,11561), (10264,548), (10733,5), (11744,6759)
X(12121) = anticomplement of X(10113)
X(12121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,7728,5655), (376,3448,12041)
The reciprocal orthologic center of these triangles is X(3).
X(12122) lies on these lines: {2,6249}, {3,83}, {4,6292}, {20,1352}, {30,6287}, {35,10064}, {36,10080}, {98,5188}, {99,550}, {165,9903}, {376,754}, {382,7910}, {511,7839}, {517,7977}, {574,3528}, {631,6704}, {732,1350}, {3522,9737}, {3529,3734}, {6274,11825}, {6275,11824}, {8150,8722}, {8993,9540}, {9918,11414}
X(12122) = midpoint of X(20) and X(2896)
X(12122) = reflection of X(i) in X(j) for these (i,j): (4,6292), (83,3), (8725,550)
X(12122) = anticomplement of X(6249)
X(12122) = X(83)-of-ABC-X3-reflections-triangle
X(12122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,83,9751), (5188,7470,98)
The reciprocal orthologic center of these triangles is X(3).
X(12123) lies on these lines: {2,6251}, {3,486}, {4,642}, {20,487}, {30,6290}, {35,10067}, {36,10083}, {99,489}, {165,9906}, {371,7738}, {376,5860}, {485,8997}, {517,7980}, {550,1350}, {631,6119}, {1151,2549}, {2043,5473}, {2044,5474}, {3098,9986}, {6399,8182}, {6560,9732}, {9921,11414}
X(12123) = midpoint of X(20) and X(487)
X(12123) = reflection of X(i) in X(j) for these (i,j): (4,642), (486,3), (6281,487)
X(12123) = anticomplement of X(6251)
The reciprocal orthologic center of these triangles is X(3).
X(12124) lies on these lines: {2,6250}, {3,485}, {4,641}, {20,488}, {30,6289}, {35,10068}, {36,10084}, {99,490}, {165,9907}, {372,7738}, {376,5861}, {486,9739}, {517,7981}, {550,1350}, {631,6118}, {1152,2549}, {2043,5474}, {2044,5473}, {3098,9987}, {6222,8182}, {6561,9733}, {9922,11414}
X(12124) = midpoint of X(20) and X(488)
X(12124) = reflection of X(i) in X(j) for these (i,j): (4,641), (485,3), (6278,488)
X(12124) = anticomplement of X(6250)
The reciprocal orthologic center of these triangles is X(1).
X(12125) lies on these lines: {1,11678}, {2,9850}, {8,971}, {9,9846}, {63,4882}, {78,9845}, {100,9841}, {145,9848}, {200,9851}, {329,9797}, {377,5176}, {452,3890}, {519,3869}, {936,2975}, {938,3436}, {3877,12059}, {5744,9858}, {5815,6865}, {5828,9940}, {6736,11220}, {9842,11680}, {9843,11681}, {9849,11686}, {9852,11688}, {9853,11690}
X(12125) = reflection of X(i) in X(j) for these (i,j): (145,9848), (9797,9844), (9846,9), (9859,4882)
X(12125) = anticomplement of X(9850)
X(12125) = excentral-to-inner-Conway similarity image of X(4882)
The reciprocal orthologic center of these triangles is X(1).
X(12126) lies on these lines: {1,971}, {936,10882}, {938,11021}, {1764,4882}, {9797,10446}, {9841,10434}, {9842,10886}, {9843,10887}, {9844,10888}, {9846,10889}, {9849,11893}, {9852,10892}, {9853,11894}, {9858,10856}, {9859,10444}, {11679,12125}
X(12126) = excentral-to-3rd-Conway similarity image of X(4882)
The reciprocal orthologic center of these triangles is X(1).
X(12127) lies on these lines: {1,2}, {269,4460}, {517,9845}, {944,2951}, {971,7982}, {1317,1467}, {2136,3361}, {3339,3880}, {3340,9850}, {3555,9851}, {3813,5726}, {3875,7271}, {3879,7274}, {4900,5836}, {5045,11525}, {5223,9957}, {6762,9819}, {7962,9848}, {7991,9841}, {9842,11522}, {9844,11523}, {9846,11526}, {9849,11528}, {9852,11533}, {9858,11518}, {9859,11520}, {10914,10980}, {11521,12126}, {11682,12125}
X(12127) = midpoint of X(i) and X(j) for these {i,j}: {145,9797}, {9851,11531}
X(12127) = reflection of X(i) in X(j) for these (i,j): (4882,1), (7991,9841)
X(12127) = excentral-to-excenters-reflections similarity image of X(4882)
X(12127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,3632,8580), (1,11519,4915), (3241,4853,1), (3635,9623,1)
The reciprocal orthologic center of these triangles is X(1).
X(12128) lies on these lines: {1,971}, {145,10569}, {355,938}, {495,9843}, {496,3817}, {517,3600}, {519,942}, {936,999}, {3295,9841}, {3333,4882}, {3487,9844}, {3616,12125}, {3655,4313}, {4297,9957}, {4321,8158}, {4853,10855}, {5082,9797}, {6244,7091}, {9581,11237}, {9846,11038}, {9849,11040}, {9852,11043}, {11529,12127}
X(12128) = midpoint of X(1) and X(9850)
X(12128) = reflection of X(938) in X(5045)
X(12128) = excentral-to-incircle-circles similarity image of X(4882)
The reciprocal orthologic center of these triangles is X(1).
X(12129) lies on these lines: {1,10867}, {519,9808}, {936,8225}, {938,11030}, {971,7596}, {4882,8231}, {8224,9841}, {8228,9842}, {8230,9843}, {8233,9844}, {8234,9845}, {8237,9846}, {8239,9848}, {8243,9850}, {8244,9851}, {8246,9852}, {8247,9853}, {8248,9854}, {9789,9797}, {9849,11925}, {9858,10858}, {9859,10885}, {10891,12126}, {11042,12128}, {11532,12127}, {11687,12125}
X(12129) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(4882)
The reciprocal orthologic center of these triangles is X(1).
X(12130) lies on these lines: {1,11860}, {174,9850}, {936,7587}, {938,8083}, {971,8351}, {8126,12125}, {8382,9843}, {8389,9846}, {8423,9851}, {8425,9852}, {8729,9858}, {9797,11891}, {9848,11924}, {9859,11890}, {11535,12127}, {11896,12126}, {11996,12129}
X(12130) = excentral-to-Yff-central similarity image of X(4882)
The reciprocal orthologic center of these triangles is X(5999).
X(12131) lies on these lines: {4,147}, {24,12042}, {25,98}, {33,3027}, {34,3023}, {99,1593}, {114,136}, {115,235}, {132,8754}, {232,2023}, {264,5976}, {428,542}, {458,10352}, {468,6036}, {1785,5988}, {1862,2783}, {2784,5185}, {2794,3575}, {5064,6054}, {5090,9864}, {5984,6995}, {6226,11389}, {6227,11388}, {7487,9862}, {7713,9860}, {7714,11177}, {7970,11396}, {10053,11398}, {10069,11399}, {11363,11710}
X(12131) = reflection of X(5186) in X(4)
X(12131) = polar circle-inverse-of-X(147)
X(12131) = orthologic center of these triangles: anti-Ara to6th anti-Brocard, anti-Ara and 1st Brocard, anti-Ara to 6th Brocard
The reciprocal orthologic center of these triangles is X(9855).
X(12132) lies on these lines: {4,8591}, {25,671}, {30,12131}, {99,5064}, {148,7714}, {235,9880}, {427,2482}, {428,543}, {468,5461}, {542,3575}, {1593,12117}, {1843,9830}, {1907,10992}, {2782,7576}, {5090,9881}, {6995,8596}, {7713,9875}, {8541,8787}, {9878,11386}, {9882,11388}, {9883,11389}, {9884,11396}, {10054,11398}, {10070,11399}
X(12132) = reflection of X(5186) in X(428)
X(12132) = orthologic center of these triangles: anti-Ara to 2nd Hyacinth
The reciprocal orthologic center of these triangles is X(12112).
Let A'B'C' be the orthocentroidal triangle. Let A" be the orthogonal projection of A on line B'C', and define B" and C" cyclically. Triangle A"B"C" is perspective to the orthic triangle at X(12133). (Randy Hutson, July 21, 2017)X(12133) lies on these lines: {4,94}, {24,12041}, {25,74}, {33,3028}, {66,11744}, {110,1593}, {113,427}, {125,235}, {185,11746}, {378,1511}, {381,9826}, {382,7723}, {399,1597}, {428,541}, {468,6699}, {542,5186}, {690,12131}, {974,1514}, {1596,10264}, {1598,10620}, {1843,2781}, {1862,2771}, {1900,2779}, {2772,5185}, {2777,3575}, {2931,11472}, {5064,10706}, {6143,11017}, {7713,9904}, {7725,11388}, {7726,11389}, {7978,11396}, {9984,11386}, {10065,11398}, {10081,11399}, {10628,11576}, {10721,11387}, {11363,11709}
X(12133) = midpoint of X(i) and X(j) for these {i,j}: {125,11381}, {382,7723}
X(12133) = reflection of X(i) in X(j) for these (i,j): (185,11746), (974,7687), (1112,4)
X(12133) = polar circle-inverse-of-X(146)
X(12133) = intersection of tangents to Walsmith rectangular hyperbola at X(74) and X(113)
X(12133) = orthologic center of these triangles: anti-Ara to orthocentroidal
X(12133) = {X(974), X(7687)}-harmonic conjugate of X(12099)
The reciprocal orthologic center of these triangles is X(9833).
X(12134) lies on these lines: {2,9707}, {3,66}, {4,155}, {5,156}, {6,7528}, {23,2888}, {24,11442}, {25,68}, {26,343}, {30,5562}, {49,5576}, {52,1843}, {54,5133}, {110,1594}, {113,137}, {140,5944}, {154,3549}, {182,7405}, {235,9927}, {381,11426}, {389,542}, {427,1147}, {428,539}, {468,5449}, {511,7553}, {524,6243}, {568,11745}, {578,3818}, {1069,11393}, {1092,11550}, {1154,11819}, {1209,6676}, {1568,11572}, {1593,12118}, {1625,7745}, {1656,8780}, {1853,3548}, {1885,12133}, {1899,6642}, {3091,12022}, {3157,11392}, {3410,7488}, {3518,3580}, {3547,11206}, {5072,12024}, {5090,9928}, {5169,9545}, {5447,7667}, {5462,10116}, {5654,7507}, {5889,7576}, {5891,11750}, {5921,7487}, {6240,12111}, {6288,10024}, {6639,10192}, {6776,7401}, {6800,7558}, {7491,10454}, {7542,10282}, {7544,7592}, {7565,9143}, {7713,9896}, {9306,11585}, {9730,9825}, {9923,11386}, {9929,11388}, {9930,11389}, {9933,11396}, {10055,11398}, {10071,11399}, {10095,11264}, {10110,10112}, {10111,11746}, {10295,11440}
X(12134) = midpoint of X(6240) and X(12111)
X(12134) = reflection of X(i) in X(j) for these (i,j): (52,6756), (6146,5), (10111,11746), (10112,10110), (10116,5462), (11264,10095)
X(12134) = complement of X(34224)
X(12134) = crosspoint, wrt excentral or tangential triangle, of X(155) and X(2918)
X(12134) = orthologic center of these triangles: anti-Ara to 2nd Hyacinth
X(12134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,1594,9820), (578,3818,7403), (1352,9833,3), (5462,10116,11245), (5921,7487,11411), (6288,10540,10024)
The reciprocal orthologic center of these triangles is X(10).
X(12135) lies on these lines: {1,427}, {4,145}, {8,25}, {10,468}, {24,5690}, {27,6542}, {28,4720}, {29,7140}, {33,1904}, {34,5101}, {235,355}, {407,5174}, {428,519}, {429,6198}, {431,5086}, {469,4393}, {515,1885}, {517,3575}, {594,1474}, {944,1593}, {1398,3476}, {1483,1595}, {1594,5901}, {1824,1891}, {1826,1990}, {1843,5846}, {1870,1883}, {1876,10106}, {1892,3340}, {1906,5881}, {1973,4390}, {2098,11393}, {2099,11392}, {2204,5291}, {2356,10459}, {3088,7967}, {3189,11406}, {3241,5064}, {3486,7071}, {3515,5657}, {3516,5731}, {3541,10246}, {3542,5790}, {3616,5094}, {3617,6353}, {3621,6995}, {3622,8889}, {3623,7378}, {3632,7713}, {3913,11383}, {4232,4678}, {5603,7507}, {5844,6756}, {10573,11399}, {10912,11390}
X(12135) = reflection of X(1885) in X(1902)
X(12135) = orthologic center of these triangles: anti-Ara to 2nd Schiffler
X(12135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5090,427), (4,145,11396), (8,7718,25), (10,11363,468), (33,5130,1904), (5174,7009,407)
The reciprocal orthologic center of these triangles is X(40).
X(12136) lies on these lines: {4,7}, {25,84}, {34,1854}, {185,1829}, {235,6245}, {406,10167}, {427,6260}, {429,9942}, {451,11227}, {468,6705}, {475,5927}, {515,1885}, {1490,1593}, {1709,11398}, {1870,9856}, {3088,5658}, {4194,11220}, {6257,11389}, {6258,11388}, {7713,7992}, {7971,11396}, {10085,11399}, {11363,12114}
The reciprocal orthologic center of these triangles is X(3).
X(12137) lies on these lines: {4,6224}, {11,11363}, {25,80}, {100,5090}, {149,7718}, {214,427}, {468,6702}, {515,1878}, {952,1829}, {1593,12119}, {1862,1900}, {1902,5840}, {2800,3575}, {2802,12135}, {2829,12136}, {6262,11389}, {6263,11388}, {7713,9897}, {7972,11396}, {10057,11398}, {10073,11399}
The reciprocal orthologic center of these triangles is X(40).
X(12138) lies on these lines: {4,145}, {11,34}, {25,104}, {33,1317}, {80,1041}, {100,1593}, {119,427}, {468,6713}, {515,1878}, {1112,2771}, {1387,1870}, {1484,1596}, {1595,11698}, {1768,7713}, {1828,2829}, {1829,2800}, {1861,3036}, {1885,5840}, {1890,5851}, {1902,2802}, {1904,6265}, {1905,11570}, {1907,5130}, {2783,5186}, {2787,12131}, {2801,5185}, {4219,9945}, {5064,10711}, {5155,6326}, {6154,11471}, {10058,11398}, {10074,11399}, {11363,11715}
X(12138) = reflection of X(1862) in X(4)
X(12138) = polar circle-inverse-of-X(153)
The reciprocal orthologic center of these triangles is X(40).
X(12139) lies on these lines: {4,9874}, {25,7160}, {1593,12120}, {1824,12136}, {7713,9898}, {8000,11396}, {10059,11398}, {10075,11399}
The reciprocal orthologic center of these triangles is X(6102).
X(12140) lies on these lines: {4,110}, {24,125}, {25,265}, {30,12133}, {66,74}, {186,6699}, {235,10113}, {378,3818}, {403,1495}, {427,1511}, {542,1843}, {974,1503}, {1112,6756}, {1593,12121}, {1594,5972}, {2771,12137}, {2777,6240}, {3448,7487}, {3575,5663}, {6146,11746}, {6403,7731}, {6723,10018}, {7505,11750}, {7577,10546}, {7722,11387}, {10088,11392}, {10091,11393}
X(12140) = reflection of X(i) in X(j) for these (i,j): (1112,6756), (6146,11746)
X(12140) = polar-circle inverse of X(39118)
The reciprocal orthologic center of these triangles is X(3).
X(12141) lies on these lines: {4,617}, {14,25}, {24,6774}, {115,10641}, {235,5479}, {427,619}, {428,531}, {462,6110}, {468,6670}, {530,12132}, {542,1843}, {1593,5474}, {3439,3456}, {5064,5464}, {5471,10642}, {6269,11389}, {6271,11388}, {6773,7487}, {7713,9900}, {7974,11396}, {9113,11409}, {9981,11386}, {10061,11398}, {10077,11399}, {11363,11706}
X(12141) = {X(1843),X(7576)}-harmonic conjugate of X(12142)
The reciprocal orthologic center of these triangles is X(3).
X(12142) lies on these lines: {4,616}, {13,25}, {24,6771}, {115,10642}, {235,5478}, {427,618}, {428,530}, {463,6111}, {468,6669}, {531,12132}, {542,1843}, {1593,5473}, {3438,3456}, {5064,5463}, {5472,10641}, {6268,11389}, {6270,11388}, {6770,7487}, {7713,9901}, {7975,11396}, {9112,11408}, {9982,11386}, {10062,11398}, {10078,11399}, {11363,11705}
X(12142) = {X(1843),X(7576)}-harmonic conjugate of X(12141)
The reciprocal orthologic center of these triangles is X(3).
X(12143) lies on these lines: {4,147}, {25,76}, {39,427}, {235,6248}, {262,7507}, {264,11325}, {384,11380}, {428,538}, {468,3934}, {511,3575}, {730,1829}, {732,1843}, {1593,11257}, {1594,11272}, {2790,9873}, {3088,7709}, {3186,9983}, {3541,11171}, {3542,7697}, {5064,7757}, {5094,7786}, {5969,12132}, {6272,11389}, {6273,11388}, {7713,9902}, {7976,11396}, {10063,11398}, {10079,11399}
X(12143) = polar-circle-inverse of X(32528)
X(12143) = X(76)-of-anti-Ara-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12144) lies on these lines: {4,2896}, {25,83}, {235,6249}, {427,6292}, {428,754}, {468,6704}, {732,1843}, {1593,12122}, {3199,10301}, {3515,9751}, {6274,11389}, {6275,11388}, {6756,12131}, {7713,9903}, {7977,11396}, {10064,11398}, {10080,11399}
X(12144) = X(83)-of-anti-Ara-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12145) lies on these lines: {4,339}, {25,1073}, {33,3320}, {34,6020}, {51,125}, {112,1593}, {127,235}, {428,9530}, {511,1529}, {1862,2831}, {1885,2794}, {2799,12131}, {2806,12138}, {2825,5185}, {9517,12133}, {10734,10735}
The reciprocal orthologic center of these triangles is X(79).
X(12146) lies on the line {25,10266}
The reciprocal orthologic center of these triangles is X(3).
X(12147) lies on these lines: {4,487}, {25,486}, {30,6406}, {52,1843}, {235,6251}, {371,8967}, {427,642}, {468,6119}, {1593,12123}, {6280,11389}, {6281,11388}, {6995,8948}, {7713,9906}, {7980,11396}, {9986,11386}, {10067,11398}, {10083,11399}
X(12147) = {X(1843),X(6756)}-harmonic conjugate of X(12148)
The reciprocal orthologic center of these triangles is X(3).
X(12148) lies on these lines: {4,488}, {25,485}, {30,6291}, {52,1843}, {235,6250}, {427,641}, {468,6118}, {1593,12124}, {6278,11389}, {6279,11388}, {6995,8946}, {7713,9907}, {7981,11396}, {9987,11386}, {10068,11398}, {10084,11399}
X(12148) = {X(1843),X(6756)}-harmonic conjugate of X(12147)
The reciprocal orthologic center of these triangles is X(9870).
X(12149) lies on these lines: {2,9869}, {110,1296}, {512,9146}, {2854,2979}, {5077,7998}
X(12149) = 1st-tri-squares-to-anti-Artzt similarity image of X(13641)
The reciprocal orthologic center of these triangles is X(2).
X(12150) lies on these lines: {2,32}, {3,7878}, {4,7856}, {6,99}, {30,3398}, {76,11286}, {98,381}, {148,5355}, {182,376}, {187,3329}, {316,7792}, {325,8368}, {384,538}, {385,5008}, {428,11380}, {524,6661}, {530,11299}, {531,11300}, {543,4027}, {549,2080}, {551,11364}, {597,1691}, {671,3407}, {1186,3224}, {1384,7771}, {1651,11839}, {1975,7894}, {1992,5039}, {3053,7786}, {3058,10799}, {3241,10800}, {3524,5171}, {3545,10358}, {3552,7772}, {3589,7831}, {3679,10789}, {3734,7766}, {3788,7921}, {3849,7924}, {4234,4279}, {4421,11490}, {5038,8598}, {5041,7783}, {5055,10104}, {5304,11185}, {5306,8370}, {5475,7806}, {5860,10793}, {5861,10792}, {6179,7770}, {6573,6579}, {6655,7829}, {6658,7765}, {7669,11327}, {7737,7790}, {7745,7828}, {7747,7797}, {7748,7920}, {7750,7859}, {7759,7892}, {7761,7875}, {7762,7832}, {7768,7819}, {7773,7942}, {7774,7835}, {7776,7930}, {7778,7926}, {7779,7820}, {7782,9605}, {7784,7943}, {7789,7905}, {7795,7877}, {7799,8369}, {7801,7837}, {7802,7803}, {7807,7858}, {7816,7839}, {7822,7893}, {7823,7834}, {7825,7932}, {7836,7838}, {7840,7880}, {7841,7884}, {7842,7923}, {7843,7901}, {7845,7931}, {7847,8353}, {7850,7868}, {7852,7885}, {7854,10159}, {7860,7866}, {7869,7946}, {7870,9766}, {7873,7948}, {7874,7941}, {7881,7949}, {7898,7913}, {7903,7945}, {7915,7939}, {8703,12054}, {9909,10790}, {10056,10801}, {10072,10802}, {10794,11235}, {10795,11236}, {10797,11237}, {10798,11238}, {10803,11239}, {10804,11240}, {11057,11287}, {11163,11288}, {11207,11837}, {11208,11838}
X(12150) = reflection of X(7883) in X(2)
X(12150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,7812,7809), (2,9939,7865), (6,1003,7757), (6,3972,99), (32,83,1078), (32,7787,83), (32,7808,7793), (32,10348,10347), (315,7846,7944), (316,7792,7919), (384,5007,7760), (1003,7757,99), (1384,11174,7771), (3972,7757,1003), (5008,7804,385), (5309,11361,671), (6680,7785,7899), (7759,7892,7909), (7762,7832,7917), (10796,11842,98)
X(12150) = X(2)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(8593).
X(12151) lies on these lines: {2,2056}, {6,538}, {83,11054}, {99,8586}, {182,599}, {183,10485}, {249,524}, {542,2456}, {575,9466}, {2080,2482}, {3398,7801}, {4027,7840}, {5026,5104}, {5111,5969}, {7809,8593}, {7810,12054}, {7839,9887}, {8584,12150}, {9939,10131}
X(12151) = midpoint of X(7809) and X(8593)
X(12151) = reflection of X(1691) in X(5182)
The reciprocal orthologic center of these triangles is X(2).
X(12152) lies on these lines: {2,493}, {30,9838}, {376,11828}, {381,8212}, {428,11394}, {551,11377}, {1651,11907}, {3058,11947}, {3241,8210}, {3679,8188}, {4421,11503}, {5860,8218}, {5861,8216}, {6461,12153}, {7811,10875}, {8194,9909}, {8201,11207}, {8208,11208}, {10056,11951}, {10072,11953}, {10945,11235}, {10951,11236}, {11237,11930}, {11238,11932}, {11239,11955}, {11240,11957}, {11840,12150}
The reciprocal orthologic center of these triangles is X(2).
X(12153) lies on these lines: {2,494}, {30,9839}, {376,11829}, {381,8213}, {428,11395}, {551,11378}, {1505,8222}, {1651,11908}, {3058,11948}, {3241,8211}, {3679,8189}, {4421,11504}, {5860,8219}, {5861,8217}, {6461,12152}, {7811,10876}, {8195,9909}, {8202,11207}, {8209,11208}, {10056,11952}, {10072,11954}, {10946,11235}, {10952,11236}, {11237,11931}, {11238,11933}, {11239,11956}, {11240,11958}, {11841,12150}
The reciprocal orthologic center of these triangles is X(9761).
X(12154) lies on these lines: {2,14}, {6,543}, {13,11317}, {16,8598}, {17,10809}, {61,8370}, {99,9113}, {395,9886}, {396,3363}, {398,8369}, {530,8593}, {542,11295}, {597,6775}, {1003,9114}, {2482,5471}, {5339,11318}, {5475,9117}, {5476,11296}, {6772,9830}, {8595,9116}
X(12154) = reflection of X(6775) in X(597)
X(12154) = Napoleon-outer circle-inverse-of-X(9760)
X(12154) = {X(6), X(11159)}-harmonic conjugate of X(12155)
The reciprocal orthologic center of these triangles is X(9763).
X(12155) lies on these lines: {2,13}, {6,543}, {14,11317}, {15,8598}, {18,10808}, {62,8370}, {99,9112}, {395,3363}, {396,9885}, {397,8369}, {531,8593}, {542,11296}, {597,6772}, {1003,9116}, {2482,5472}, {5340,11318}, {5475,9115}, {5476,11295}, {6775,9830}, {8594,9114}
X(12155) = reflection of X(6772) in X(597)
X(12155) = Napoleon-inner circle-inverse-of-X(9762)
X(12155) = {X(6), X(11159)}-harmonic conjugate of X(12154)
The reciprocal orthologic center of these triangles is X(9766).
X(12156) lies on these lines: {2,32}, {3845,11632}, {3972,9766}, {4677,9903}, {5066,6287}, {5097,10723}, {5306,9166}, {7760,11361}, {7878,11287}, {8584,8593}, {8703,12122}, {9300,11155}, {9751,12100}, {11055,11159}, {11149,11163}
X(12156) = {X(7812), X(12150)}-harmonic conjugate of X(7809)
The reciprocal orthologic center of these triangles is X(2).
X(12157) lies on the anti-Artzt circle and these lines: {99,511}, {110,5104}, {512,11161}, {805,2770}, {6787,11178}, {10717,12149}
X(12157) = circumsymmedial-to-anti-Artzt similarity image of X(2698)
The reciprocal orthologic center of these triangles is X(591).
X(12158) lies on these lines: {2,371}, {8584,11159}
X(12158) = X(1328)-of-anti-Artzt-triangle
X(12158) = {X(8584),X(11159)}-harmonic conjugate of X(12159)
The reciprocal orthologic center of these triangles is X(1991).
X(12159) lies on these lines: {2,372}, {1991,6390}, {8584,11159}
X(12159) = X(1327)-of-anti-Artzt-triangle
X(12159) = {X(8584),X(11159)}-harmonic conjugate of X(12158)
The reciprocal orthologic center of these triangles is X(11412).
X(12160) lies on these lines: {2,11432}, {3,54}, {4,193}, {5,6515}, {6,5562}, {24,3167}, {25,52}, {68,7507}, {69,7399}, {110,3517}, {143,7529}, {156,9714}, {184,9715}, {389,394}, {427,11411}, {511,1181}, {568,6090}, {576,5907}, {912,11396}, {1092,9786}, {1147,3515}, {1199,5050}, {1216,7484}, {1350,10984}, {1398,7352}, {1498,2393}, {1597,12111}, {1598,3060}, {1614,9909}, {1656,3580}, {1994,7503}, {3091,3527}, {3410,7566}, {3518,8780}, {3567,5020}, {3575,6193}, {5059,11820}, {5093,11459}, {5198,5446}, {5410,10665}, {5411,10666}, {5422,11444}, {5462,11284}, {5640,11484}, {6146,10602}, {6237,11406}, {6238,7071}, {6243,7387}, {6643,11245}, {7689,11410}, {8548,11405}, {9936,12134}, {10601,11793}, {10661,11408}, {10662,11409}
X(12160) = reflection of X(11414) in X(1181)
X(12160) = orthologic center of anti-Ascella triangle to these triangles: anti-Conway, 2nd anti-Conway, 3rd anti-Euler, 3rd anti-Euler, anti-excenters-reflections, anti-Hutson intouch, anti-incircle-circles, anti-inverse-in-incircle, 6th anti-mixtilinear, circumorthic, 2nd Ehrmann, 2nd Euler, extangents, intangents, 1st Kenmotu diagonals, 2nd Kenmotu diagonals, Kosnita, orthic, submedial, tangential, inner tri-equilateral, outer tri-equilateral, Trinh.
X(12160) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,5562,7395), (52,155,25), (576,5907,10982), (1199,7509,5050), (1993,5889,3), (1994,7503,11426), (3060,11441,1598), (7592,11412,3)
The reciprocal orthologic center of these triangles is X(12160).
X(12161) lies on these lines: {2,1199}, {3,54}, {4,1994}, {5,6}, {20,11004}, {22,6243}, {24,49}, {25,143}, {26,52}, {30,1181}, {51,10539}, {81,6862}, {110,3567}, {140,394}, {182,1216}, {185,12084}, {186,9545}, {193,3547}, {265,7547}, {323,631}, {381,11441}, {382,11456}, {389,1147}, {399,3843}, {546,10982}, {567,7503}, {569,5562}, {575,11793}, {576,2393}, {578,7526}, {895,3527}, {1092,9730}, {1184,10011}, {1351,7387}, {1498,3627}, {1593,5663}, {1598,5093}, {1614,3060}, {1656,5422}, {2070,9704}, {2914,3448}, {2937,6800}, {3167,5946}, {3193,6928}, {3518,9544}, {3549,6515}, {3574,7564}, {3580,6639}, {3618,11487}, {3628,10601}, {3796,7525}, {5050,7393}, {5097,10110}, {5462,9306}, {5576,11442}, {5876,9818}, {6237,11428}, {6238,11429}, {7395,11591}, {7507,11264}, {7512,11003}, {7529,9777}, {7689,11430}, {9587,9625}, {9590,9622}, {9706,11464}, {9833,11819}, {9927,10112}, {10115,10274}, {10540,10594}, {10602,11255}, {10605,11250}, {10625,10984}, {11245,11585}, {11411,11427}, {11438,12038}, {11818,12134}
X(12161) = midpoint of X(3) and X(12160)
X(12161) = reflection of X(7526) in X(578)
X(12161) = X(3)-of-2nd-anti-extouch-triangle
X(12161) = X(4)-of-anti-Conway-triangle
X(12161) = X(5)-of-anti-Ascella-triangle
X(12161) = anti-Conway-isogonal conjugate of X(32046)
X(12161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,195,1993), (6,155,5), (49,568,24), (52,184,26), (54,5889,3), (110,3567,7506), (143,156,25), (182,1216,7516), (389,1147,6644), (569,5562,7514), (576,6759,5446), (1351,7387,10263), (1614,3060,7517), (1993,7592,3), (2070,9704,9707), (5012,11412,3), (5446,6759,7530), (5889,11422,54), (11402,12160,3), (11412,11423,5012)
The reciprocal orthologic center of these triangles is X(12160).
Let T be the triangle whose vertices are the orthocenters of the altimedial triangles; then X(12162) = X(20)-of-T. (Randy Hutson, July 21, 2017)
X(12162) lies on these lines: {2,6241}, {3,64}, {4,52}, {5,113}, {20,1216}, {24,7689}, {30,5562}, {33,7352}, {34,6238}, {39,1625}, {49,399}, {51,546}, {54,7527}, {67,3521}, {110,3520}, {143,3845}, {155,1593}, {184,7526}, {186,11440}, {355,2807}, {376,5447}, {378,1147}, {381,389}, {382,511}, {394,12085}, {403,5449}, {517,6253}, {550,3917}, {568,3843}, {569,1181}, {631,10170}, {912,1902}, {1060,7355}, {1062,6285}, {1092,10564}, {1154,3627}, {1204,6644}, {1209,2883}, {1352,5878}, {1495,1658}, {1503,9967}, {1511,10226}, {1531,11572}, {1594,5448}, {1656,9729}, {2772,5884}, {2777,7723}, {2979,3529}, {3090,5892}, {3091,5462}, {3146,11412}, {3522,7999}, {3528,7998}, {3530,5650}, {3541,5654}, {3544,11451}, {3547,5656}, {3567,3832}, {3830,6243}, {3839,9781}, {3850,5946}, {3851,5943}, {3853,10263}, {3855,5640}, {3858,10095}, {4550,7503}, {4846,6815}, {5055,11695}, {5079,6688}, {5498,10272}, {6193,11469}, {6237,11471}, {6247,11585}, {6254,8251}, {6288,7728}, {6636,8718}, {6642,10605}, {6696,10257}, {7506,11438}, {7512,12112}, {7514,10984}, {7529,9786}, {7544,7706}, {7691,12088}, {7722,11557}, {8538,8549}, {8548,11470}, {10116,12022}, {10634,10675}, {10635,10676}, {10661,11475}, {10662,11476}, {10665,11473}, {10666,11474}, {10996,11487}, {11403,12160}, {11424,12161}
X(12162) = midpoint of X(i) and X(j) for these {i,j}: {4,12111}, {3146,11412}, {5562,11381}
X(12162) = reflection of X(i) in X(j) for these (i,j): (3,5907), (20,1216), (52,4), (185,5), (550,11591), (5562,5876), (5889,5446), (6102,546), (7722,11557), (10263,3853), (10575,3), (10625,5562), (11562,113)
X(12162) = complement of X(6241)
X(12162) = X(4)-of-X(4)-Brocard-triangle
X(12162) = X(10)-of-Ehrmann-side-triangle if ABC is acute" to X(12162)
X(12162) = X(10)-of-Ehrmann-side-triangle if ABC is acute
X(12162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,5907,5891), (3,10540,10282), (4,5889,5446), (4,11442,9927), (5,185,9730), (5,12006,373), (20,11459,1216), (110,3520,12038), (155,11472,1593), (376,11444,5447), (378,11441,1147), (546,6102,51), (550,11591,3917), (568,3843,10110), (3357,9306,3), (5446,5889,52), (5876,11381,10625), (5889,11439,4), (5891,10575,3), (11439,12111,5889)
The reciprocal orthologic center of these triangles is X(12160).
X(12163) lies on these lines: {3,49}, {4,3580}, {5,9786}, {6,6102}, {20,11411}, {22,6241}, {24,12111}, {25,12162}, {26,1498}, {30,64}, {35,3157}, {36,1069}, {40,912}, {52,1593}, {55,7352}, {56,6238}, {74,9938}, {140,5646}, {154,1658}, {186,11441}, {376,6193}, {378,5889}, {381,5449}, {382,9927}, {389,9818}, {511,3357}, {539,3534}, {548,9936}, {550,1350}, {568,10982}, {631,9820}, {1151,10665}, {1152,10666}, {1154,10606}, {1192,5876}, {1597,5446}, {1656,5448}, {1657,10620}, {1993,3520}, {3066,3851}, {3515,10539}, {3516,12160}, {3532,5504}, {3579,9928}, {3581,7517}, {4550,5462}, {4846,6823}, {5584,6237}, {5890,7503}, {5907,6642}, {6000,7387}, {6200,8909}, {6240,11442}, {6284,10071}, {6285,9645}, {6445,8912}, {7354,10055}, {7393,9729}, {7488,7712}, {7509,10574}, {7691,10323}, {8548,11477}, {8567,11250}, {9707,10298}, {9937,10575}, {10661,11480}, {10662,11481}, {11425,12161}
X(12163) = midpoint of X(20) and X(11411)
X(12163) = reflection of X(i) in X(j) for these (i,j): (3,7689), (155,3), (382,9927), (1498,26), (5504,12041), (9928,3579), (11477,8548), (12085,3357), (12118,550)
X(12163) = ABC-X3-reflections-isogonal conjugate of X(33495)
X(12163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,3167,12038), (74,11412,11413), (1204,5562,3), (4550,5462,11479), (5889,11440,378), (5907,11438,6642), (6102,7526,6)
Let A'B'C' be the orthic triangle. Let Oa be the A-power circle of triangle AB'C', and define Ob and Oc cyclically. X(12164) is the radical center of circles Oa, Ob, Oc. (Randy Hutson, July 31 2018)
The reciprocal orthologic center of these triangles is X(12160).
X(12164) lies on these lines: {3,49}, {4,193}, {5,11411}, {6,5907}, {24,8780}, {25,5889}, {30,6193}, {52,1598}, {68,381}, {69,6823}, {110,3515}, {235,6515}, {323,11413}, {382,9936}, {389,5020}, {399,7517}, {511,1498}, {524,2883}, {539,3830}, {568,7529}, {912,1482}, {916,2293}, {999,1069}, {1154,7387}, {1593,1993}, {1597,12162}, {1614,9715}, {1619,6293}, {1656,5544}, {1657,11820}, {2070,9932}, {2781,9914}, {3060,5198}, {3091,9777}, {3311,10665}, {3312,10666}, {3517,10539}, {3526,9820}, {3843,9927}, {3851,5448}, {5050,7395}, {5055,5449}, {5093,10982}, {5462,11484}, {5504,10620}, {5663,12085}, {5876,9818}, {6102,6642}, {6221,8909}, {6237,10306}, {6759,9909}, {6800,7691}, {6816,11245}, {7393,11591}, {7484,11444}, {7503,11402}, {7507,11442}, {7509,12017}, {8548,11482}, {8681,11477}, {8718,11412}, {9306,9786}, {9654,10055}, {9669,10071}, {9714,10540}, {9925,12082}, {10661,11485}, {10662,11486}, {11410,11440}
X(12164) = reflection of X(i) in X(j) for these (i,j): (3,155), (1657,12118), (6391,1351), (10620,5504), (11411,5), (12163,1147)
X(12164) = X(64)-Ceva conjugate of X(3)
X(12164) = X(10864)-of-orthic-triangle if ABC is acute
X(12164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,155,3167), (4,12160,1351), (6,5907,11479), (155,12163,1147), (185,394,3), (1069,7352,999), (1092,10605,3), (1147,12163,3), (1181,5562,3), (1993,12111,1593), (3157,6238,3295), (5889,11441,25), (7395,7592,5050), (7592,11459,7395), (11412,11456,11414)
The reciprocal orthologic center of these triangles is X(3581).
X(12165) lies on these lines: {3,3043}, {4,11703}, {25,399}, {74,11410}, {110,3515}, {155,11562}, {378,2914}, {1112,5198}, {1181,10628}, {1351,10733}, {1593,5663}, {2771,11396}, {3448,7507}, {3516,10620}, {5094,10264}, {7071,7727}, {7395,7723}, {7687,9777}, {7724,11406}, {7731,9919}, {9826,11284}, {9976,11405}, {10657,11408}, {10658,11409}
X(12165) = orthologic center of these triangles: anti-Ascella to orthic
X(12165) = {X(399), X(1986)}-harmonic conjugate of X(25)
The reciprocal orthologic center of these triangles is X(7387).
X(12166) lies on these lines: {3,69}, {25,52}, {68,7395}, {578,8681}, {912,8192}, {1147,5892}, {1154,7387}, {3167,5946}, {3515,9932}, {6391,11426}, {7071,9931}, {9715,9908}, {9820,11284}, {9926,11405}, {9938,11410}, {10659,11408}, {10660,11409}
X(12166) = reflection of X(12160) in X(155)
X(12166) = orthologic center of these triangles: anti-Ascella to 2nd Hyacinth
X(12166) = {X(155), X(9937)}-harmonic conjugate of X(25)
The reciprocal orthologic center of these triangles is X(576).
X(12167) lies on these lines: {3,6403}, {4,193}, {6,25}, {24,5050}, {69,427}, {141,5094}, {182,3515}, {186,12017}, {399,2971}, {428,1992}, {458,3186}, {460,3087}, {468,3618}, {511,1593}, {518,11396}, {524,3867}, {542,12165}, {576,5198}, {895,1112}, {1154,1597}, {1350,3516}, {1352,7507}, {1353,6756}, {1398,1469}, {1598,5093}, {1829,3751}, {1862,10755}, {2207,5052}, {3056,7071}, {3089,3527}, {3098,11410}, {3575,6776}, {3620,8889}, {3779,11406}, {5017,8778}, {5020,11416}, {5032,7714}, {5039,11380}, {5090,5847}, {5102,11470}, {5107,5140}, {5185,10756}, {5186,10754}, {6090,11188}, {7395,9967}, {7484,9813}, {7487,11432}, {7529,11255}, {8593,12132}, {9307,12110}, {9732,11395}, {9733,11394}, {9737,10607}, {9822,11284}, {10594,11482}, {10752,12133}, {10753,12131}, {10759,12138}, {11382,11433}, {11403,11477}
X(12167) = reflection of X(12160) in X(1351)
X(12167) = homothetic center of orthic triangle and reflection of tangential triangle in X(6)
X(12167) = {X(12171),X(12172)}-harmonic conjugate of X(1593)
X(12167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,1843,25), (6,7716,1974), (6,9924,184), (6,9973,159), (25,8541,11405), (1351,6391,193), (1843,1974,7716), (1843,8541,6), (1974,7716,25), (5410,11389,25), (5411,11388,25)
The reciprocal orthologic center of these triangles is X(10112).
X(12168) lies on these lines: {3,74}, {22,146}, {25,113}, {125,7395}, {159,2935}, {265,9818}, {1597,10733}, {1657,8907}, {2777,11414}, {3028,10832}, {3043,3167}, {3448,7503}, {6644,10272}, {6699,7484}, {7387,7728}, {7514,10264}, {9715,10117}, {9909,10706}, {10663,11408}, {10664,11409}, {10982,11800}, {11562,12163}, {12085,12121}
X(12168) = {X(113), X(2931)}-harmonic conjugate of X(25)
The reciprocal orthologic center of these triangles is X(3).
X(12169) lies on these lines: {25,487}, {486,7484}, {642,11284}, {3564,11414}, {5198,6290}
X(12169) = orthic-to-anti-Ascella similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12170) lies on these lines: {25,488}, {485,7484}, {641,11284}, {3564,11414}, {5198,6289}
X(12170) = orthic-to-anti-Ascella similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12171) lies on these lines: {3,6239}, {25,1151}, {511,1593}, {1398,7362}, {5023,5413}, {5411,8778}, {6200,8948}, {6252,11406}, {6283,7071}, {7690,11410}, {9732,11394}, {9823,11284}, {9974,11405}, {10667,11408}, {10668,11409}
X(12171) = {X(1593),X(12167)}-harmonic conjugate of X(12172)
X(12171) = X(176)-of-anti-Ascella-triangle if ABC is acute
X(12171) = orthic-to-anti-Ascella similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12172) lies on these lines: {3,6400}, {25,1152}, {511,1593}, {1398,7353}, {5023,5412}, {5410,8778}, {6396,8946}, {6404,11406}, {6405,7071}, {7692,11410}, {9733,11395}, {9824,11284}, {9975,11405}, {10671,11408}, {10672,11409}
X(12172) = {X(1593),X(12167)}-harmonic conjugate of X(12171)
X(12172) = X(175)-of-anti-Ascella-triangle if ABC is acute
X(12172) = orthic-to-anti-Ascella similarity image of X(6406)
As a point on the Euler line, X(12173) has Shinagawa coefficients: (-F, E+5*F).
X(12173) lies on these lines: {2,3}, {33,4348}, {34,7221}, {64,6145}, {70,3426}, {125,1192}, {515,11396}, {516,5090}, {950,1892}, {962,12135}, {1112,10733}, {1204,1853}, {1398,7354}, {1503,12167}, {1699,11363}, {1829,5691}, {1843,5895}, {1862,10724}, {1870,9655}, {1876,9579}, {2207,7747}, {3070,5410}, {3071,5411}, {3172,7737}, {3574,11425}, {3583,11399}, {3585,11398}, {5185,10725}, {5186,10723}, {5318,11408}, {5321,11409}, {5339,8739}, {5340,8740}, {5890,6746}, {6198,9668}, {6241,7730}, {6253,11391}, {6256,11400}, {6284,7071}, {6403,12111}, {7718,9812}, {7728,12140}, {7823,9308}, {8550,11405}, {10721,11387}, {10722,12131}, {10728,12138}, {11432,12022}
X(12173) = reflection of X(i) in X(j) for these (i,j): (20,6823), (1593,4)
X(12173) = homothetic center of orthic triangle and reflection of tangential triangle in X(4)
X(12173) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,4,7507), (4,20,427), (4,24,381), (4,186,7547), (4,403,3843), (4,1593,5064), (4,1885,11403), (4,3089,10151), (4,3146,1885), (4,3542,546), (4,3575,25), (4,6240,3), (4,6353,3832), (4,6622,3839), (4,6756,5198), (4,6995,1906), (4,7487,235), (4,7576,1598), (1596,3853,4), (1598,3830,4), (3627,6756,4)
The reciprocal orthologic center of these triangles is X(389).
X(12174) lies on these lines: {3,74}, {4,3527}, {6,9968}, {20,12164}, {25,185}, {30,12160}, {64,184}, {154,1204}, {155,10575}, {221,3270}, {235,5656}, {381,11457}, {389,5198}, {569,11472}, {578,1181}, {1192,1495}, {1351,3146}, {1398,7355}, {1425,2192}, {1503,12167}, {1597,7592}, {1598,5890}, {1885,6225}, {1899,2883}, {1906,11433}, {2777,12165}, {2807,8192}, {3167,11413}, {3357,11410}, {3426,11426}, {3515,6759}, {3529,11820}, {4846,12134}, {5020,10574}, {5093,11458}, {5094,6247}, {5095,5895}, {5422,11439}, {5878,6146}, {5907,7484}, {6001,11396}, {6199,11462}, {6254,11406}, {6285,7071}, {6293,9914}, {6395,11463}, {6767,11461}, {7395,12162}, {7722,9919}, {8549,11405}, {9715,12163}, {9729,11284}, {10594,12112}, {10675,11408}, {10676,11409}, {11414,12166}
X(12174) = reflection of X(1593) in X(1181)
X(12174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,11441,6090), (6,11381,11403), (74,9707,3), (185,1498,25), (1181,1593,11402), (6241,11456,3), (6759,10605,3515), (6800,11440,3)
The reciprocal orthologic center of these triangles is X(6243).
X(12175) lies on these lines: {3,6242}, {25,195}, {54,3515}, {539,12160}, {1154,1593}, {1351,5198}, {1398,7356}, {1614,9920}, {2888,7507}, {2914,10594}, {5965,12167}, {6255,11406}, {6286,7071}, {7691,11410}, {9827,11284}, {9977,11405}, {10677,11408}, {10678,11409}, {12165,12173}
X(12175) = {X(195), X(6152)}-harmonic conjugate of X(25)
The reciprocal orthologic center of these triangles is X(5999).
X(12176) lies on these lines: {3,1916}, {4,32}, {83,114}, {99,182}, {147,7787}, {384,2782}, {542,12150}, {1078,6036}, {1691,11676}, {2080,5999}, {2966,6784}, {3027,10799}, {3407,9755}, {5025,10104}, {5039,10753}, {6033,10796}, {6226,10793}, {6227,10792}, {7970,10800}, {9860,10789}, {9861,10790}, {9864,10791}, {10053,10801}, {10069,10802}, {10352,10359}, {11361,11632}, {11364,11710}, {11380,12131}
X(12176) = midpoint of X(98) and X(12110)
X(12176) = reflection of X(4027) in X(3398)
The reciprocal orthologic center of these triangles is X(147).
X(12177) lies on these lines: {2,98}, {3,5026}, {5,5038}, {6,2782}, {30,12151}, {32,5477}, {83,575}, {99,511}, {115,5034}, {194,576}, {381,9830}, {385,9772}, {524,2080}, {597,11632}, {611,3023}, {613,3027}, {671,5476}, {690,9970}, {1351,5969}, {1428,10069}, {1469,10089}, {1503,2456}, {1569,5028}, {1691,3564}, {1992,10788}, {2330,10053}, {2482,8722}, {2770,6233}, {2793,5652}, {3056,10086}, {3398,8550}, {3926,5171}, {5085,12042}, {5286,10358}, {5480,6321}, {5655,10748}, {5999,8289}, {7808,11623}, {8787,11842}, {9863,10131}, {10350,11257}
X(12177) = midpoint of X(i) and X(j) for these {i,j}: {99,10753}, {147,6776}, {6054,8593}
X(12177) = reflection of X(i) in X(j) for these (i,j): (3,5026), (98,182), (671,5476), (1352,114), (6321,5480), (10754,576), (11161,11178), (11632,597), (11646,5)
X(12177) = X(4)-of-6th-anti-Brocard triangle
X(12177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (98,5182,182), (147,4027,98)
X(12177) = perspector of 6th anti-Brocard triangle and 1st Brocard-reflected triangle
The reciprocal orthologic center of these triangles is X(5999).
X(12178) lies on these lines: {3,11711}, {35,9860}, {55,98}, {56,7970}, {99,10310}, {100,147}, {114,1376}, {115,11496}, {197,9861}, {542,4421}, {1001,6036}, {2782,11248}, {2784,8715}, {2794,11500}, {3023,11509}, {3295,11710}, {4428,6055}, {5687,9864}, {6033,11499}, {6226,11498}, {6227,11497}, {9862,11491}, {10053,11507}, {10069,11508}, {10267,12042}, {11383,12131}, {11490,12176}
The reciprocal orthologic center of these triangles is X(5999).
X(12179) lies on these lines: {55,12180}, {98,5597}, {99,11822}, {114,5599}, {115,8196}, {147,5601}, {542,11207}, {2782,11252}, {3027,11873}, {5598,7970}, {6033,8200}, {6226,8199}, {6227,8198}, {8190,9861}, {8197,9864}, {9862,11843}, {10053,11877}, {10069,11879}, {11366,11710}, {11492,12178}, {11837,12176}
X(12179) = reflection of X(12180) in X(55)
The reciprocal orthologic center of these triangles is X(5999).
X(12180) lies on these lines: {55,12179}, {98,5598}, {99,11823}, {114,5600}, {115,8203}, {147,5602}, {542,11208}, {2782,11253}, {3027,11874}, {5597,7970}, {6033,8207}, {6226,8206}, {6227,8205}, {8187,9860}, {8191,9861}, {8204,9864}, {9862,11844}, {10053,11878}, {10069,11880}, {11367,11710}, {11493,12178}, {11838,12176}
X(12180) = reflection of X(12179) in X(55)
The reciprocal orthologic center of these triangles is X(5999).
X(12181) lies on these lines: {30,99}, {98,402}, {114,1650}, {115,11897}, {147,4240}, {542,1651}, {2782,11251}, {2794,12113}, {3027,11909}, {6226,11902}, {6227,11901}, {7970,11910}, {9860,11852}, {9861,11853}, {9862,11845}, {9864,11900}, {10053,11912}, {10069,11913}, {11710,11831}, {11832,12131}, {11839,12176}, {11848,12178}
X(12181) = midpoint of X(147) and X(4240)
X(12181) = reflection of X(i) in X(j) for these (i,j): (98,402), (1650,114)
The reciprocal orthologic center of these triangles is X(5999).
X(12182) lies on these lines: {11,98}, {99,11826}, {114,1376}, {115,10893}, {147,3434}, {355,6033}, {542,11235}, {2782,10525}, {2794,12114}, {3027,10947}, {6226,10920}, {6227,10919}, {7970,10944}, {9860,10826}, {9861,10829}, {9862,10785}, {9864,10914}, {10053,10523}, {10069,10948}, {10794,12176}, {11373,11710}, {11390,12131}, {11865,12179}, {11866,12180}, {11903,12181}
X(12182) = reflection of X(12178) in X(114)
X(12182) = X(98)-of-inner-Johnson-triangle
X(12182) = X(12189)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(5999).
X(12183) lies on these lines: {10,2792}, {12,98}, {72,9864}, {99,11827}, {114,958}, {115,10894}, {147,3436}, {355,6033}, {542,11236}, {2782,10526}, {2794,11500}, {3027,10953}, {6226,10922}, {6227,10921}, {6253,10722}, {7970,10950}, {9860,10827}, {9861,10830}, {9862,10786}, {10053,10954}, {10069,10523}, {10795,12176}, {11374,11710}, {11391,12131}, {11867,12179}, {11868,12180}, {11904,12181}
X(12183) = reflection of X(12182) in X(6033)
X(12183) = X(98)-of-outer-Johnson-triangle
X(12183) = X(12190)-of-inner-Johnson-triangle
The reciprocal orthologic center of these triangles is X(5999).
X(12184) lies on the inner-Johnson-Yff circle and these lines: {1,6033}, {4,3027}, {5,10069}, {12,98}, {55,2794}, {56,114}, {65,9864}, {99,7354}, {115,9650}, {147,388}, {148,5229}, {226,2784}, {495,10053}, {498,12042}, {542,611}, {620,5204}, {1317,10768}, {1388,11724}, {1478,2782}, {1569,9651}, {2023,9596}, {3028,11005}, {3029,9553}, {3044,9653}, {3085,9862}, {3585,6321}, {5261,5984}, {5434,6054}, {6226,10924}, {6227,10923}, {6284,10722}, {7970,10944}, {9578,9860}, {9861,10831}, {10797,12176}, {11375,11710}, {11392,12131}, {11501,12178}, {11869,12179}, {11870,12180}, {11905,12181}
X(12184) = reflection of X(10053) in X(495)
X(12184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,6033,12185), (147,388,3023)
The reciprocal orthologic center of these triangles is X(5999).
X(12185) lies on the outer-Johnson-Yff circle and these lines: {1,6033}, {4,3023}, {5,10053}, {11,98}, {30,10089}, {55,114}, {56,2794}, {99,6284}, {115,9665}, {147,497}, {148,5225}, {496,10069}, {499,12042}, {542,613}, {620,5217}, {1479,2782}, {1569,9664}, {2023,9599}, {2784,12053}, {3029,9554}, {3044,9666}, {3057,9864}, {3058,6054}, {3086,9862}, {3583,6321}, {3845,10054}, {5274,5984}, {5985,11680}, {6226,10926}, {6227,10925}, {7354,10722}, {7970,10950}, {9581,9860}, {9861,10832}, {10798,12176}, {11376,11710}, {11393,12131}, {11502,12178}, {11871,12179}, {11872,12180}, {11906,12181}
X(12185) = reflection of X(10069) in X(496)
X(12185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,6033,12184), (147,497,3027)
The reciprocal orthologic center of these triangles is X(5999).
X(12186) lies on these lines: {98,493}, {99,11828}, {114,8222}, {115,8212}, {147,6462}, {542,12152}, {2782,10669}, {2794,9838}, {3027,11947}, {6033,8220}, {6226,8218}, {6227,8216}, {6461,12187}, {7970,8210}, {8188,9860}, {8194,9861}, {8201,12179}, {8208,12180}, {8214,9864}, {9862,10875}, {10053,11951}, {10069,11953}, {10945,12182}, {10951,12183}, {11377,11710}, {11394,12131}, {11503,12178}, {11840,12176}, {11907,12181}, {11930,12184}, {11932,12185}
The reciprocal orthologic center of these triangles is X(5999).
X(12187) lies on these lines: {98,494}, {99,11829}, {114,8223}, {115,8213}, {147,6463}, {542,12153}, {2782,10673}, {2794,9839}, {3027,11948}, {6033,8221}, {6226,8219}, {6227,8217}, {6461,12186}, {7970,8211}, {8189,9860}, {8195,9861}, {8202,12179}, {8209,12180}, {8215,9864}, {9862,10876}, {10053,11952}, {10069,11954}, {10946,12182}, {10952,12183}, {11378,11710}, {11395,12131}, {11504,12178}, {11841,12176}, {11908,12181}, {11931,12184}, {11933,12185}
The reciprocal orthologic center of these triangles is X(5999).
X(12188) lies on the 2nd Neuberg circle, Stammler circle and these lines: {2,7711}, {3,76}, {4,5984}, {5,147}, {6,13}, {25,5986}, {30,148}, {114,1656}, {182,7697}, {355,2784}, {382,2794}, {405,5985}, {517,9860}, {538,8178}, {543,3534}, {620,5054}, {621,6770}, {622,6773}, {671,3830}, {690,10620}, {868,3448}, {999,3023}, {1281,4385}, {1569,5013}, {1597,5186}, {1598,12131}, {1657,10991}, {1916,7754}, {1995,5987}, {2023,9605}, {2070,5938}, {2407,9512}, {2482,8556}, {2793,11258}, {2925,2926}, {3027,3295}, {3029,9566}, {3044,9703}, {3095,7798}, {3398,6248}, {3407,9755}, {3526,6036}, {3564,5207}, {3673,7061}, {3934,12054}, {4027,7770}, {5026,12017}, {5050,12177}, {5055,6054}, {5070,7943}, {5073,10723}, {5092,9466}, {5093,10753}, {5790,9864}, {6226,11917}, {6227,11916}, {7470,8782}, {7517,9861}, {7751,9821}, {7790,9996}, {7803,9478}, {7902,10356}, {7913,11178}, {7970,10247}, {7983,8148}, {8591,8703}, {8596,11001}, {9418,10540}, {9654,12184}, {9669,12185}, {10246,11710}, {11849,12178}, {11875,12179}, {11876,12180}, {11911,12181}, {11928,12182}, {11929,12183}, {11949,12186}, {11950,12187}
X(12188) = midpoint of X(i) and X(j) for these {i,j}: {4,5984}, {148,9862}, {8596,11001}
X(12188) = reflection of X(i) in X(j) for these (i,j): (3,98), (99,12042), (114,11623), (147,5), (381,11632), (382,6321), (3830,671), (5073,10723), (5655,11656), (6033,115), (8148,7983), (8591,8703), (8724,6055), (9301,385)
X(12188) = circumcircle-inverse-of-X(12042)
X(12188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (98,99,12042), (99,12042,3), (115,6033,381), (148,11177,9862), (3023,10069,999), (3027,10053,3295), (6033,11632,115), (6055,8724,5054), (10104,11257,3)
The reciprocal orthologic center of these triangles is X(5999).
X(12189) lies on these lines: {1,98}, {12,12182}, {99,11248}, {114,5552}, {115,10531}, {119,10768}, {147,10528}, {542,11239}, {2782,10679}, {2794,12115}, {3023,11509}, {3027,10965}, {6033,10942}, {6226,10930}, {6227,10929}, {6256,10722}, {9861,10834}, {9862,10805}, {9864,10915}, {10803,12176}, {10955,12183}, {10956,12184}, {10958,12185}, {11400,12131}, {11881,12179}, {11882,12180}, {11914,12181}, {11955,12186}, {11956,12187}, {12000,12188}
X(12189) = reflection of X(98) in X(10053)
X(12189) = {X(98),X(7970)}-harmonic conjugate of X(12190)
The reciprocal orthologic center of these triangles is X(5999).
X(12190) lies on these lines: {1,98}, {11,12183}, {99,11249}, {114,10527}, {115,10532}, {147,10529}, {542,11240}, {2782,10680}, {2792,12053}, {2794,12116}, {3027,10966}, {6033,10943}, {6226,10932}, {6227,10931}, {9861,10835}, {9862,10806}, {9864,10916}, {10804,12176}, {10949,12182}, {10957,12184}, {10959,12185}, {11401,12131}, {11510,12178}, {11883,12179}, {11884,12180}, {11915,12181}, {11957,12186}, {11958,12187}, {12001,12188}
X(12190) = reflection of X(98) in X(10069)
X(12190) = {X(98),X(7970)}-harmonic conjugate of X(12189)
The reciprocal orthologic center of these triangles is X(9855).
X(12191) lies on these lines: {6,11152}, {30,12176}, {32,671}, {83,2482}, {98,3543}, {148,5304}, {182,12117}, {384,5969}, {542,12110}, {543,4027}, {1003,1916}, {1078,5461}, {1691,9855}, {2080,8859}, {3407,11159}, {3552,9888}, {5032,12177}, {5039,8593}, {5182,7787}, {6034,7833}, {8724,10796}, {9875,10789}, {9876,10790}, {9881,10791}, {9882,10792}, {9883,10793}, {9884,10800}, {10054,10801}, {10070,10802}, {11380,12132}
X(12191) = reflection of X(4027) in X(12150)
X(12191) = orthologic center of these triangles: 5th anti-Brocard to McCay
X(12191) = X(671)-of-5th-anti-Brocard-triangle
X(12191) = {X(7787), X(8591)}-harmonic conjugate of X(5182)
The reciprocal orthologic center of these triangles is X(12112).
X(12192) lies on these lines: {2,98}, {32,74}, {83,113}, {146,7787}, {541,12150}, {690,12176}, {1078,6699}, {1511,12054}, {2080,12041}, {2777,12110}, {3028,10799}, {3043,3203}, {3398,5663}, {5039,10752}, {7725,10792}, {7728,10796}, {7978,10800}, {9904,10789}, {9919,10790}, {10065,10801}, {10081,10802}, {10620,11842}, {11364,11709}, {11380,12133}
X(12192) = orthologic center of these triangles: 5th anti-Brocard to orthocentroidal
X(12192) = X(74)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12193) lies on these lines: {32,68}, {83,1147}, {98,9927}, {155,10796}, {182,12118}, {539,12150}, {1069,10798}, {1078,5449}, {3157,10797}, {5654,10358}, {6193,7787}, {8548,12177}, {9896,10789}, {9908,10790}, {9928,10791}, {9929,10792}, {9930,10793}, {9933,10800}, {10055,10801}, {10071,10802}, {10788,11411}, {11380,12134}
X(12193) = orthologic center of these triangles: 5th anti-Brocard to 2nd Hyacinth
X(12193) = X(68)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12194) lies on these lines: {1,32}, {3,11490}, {8,7787}, {10,82}, {31,239}, {40,182}, {55,11837}, {58,99}, {98,946}, {213,8300}, {291,5299}, {355,10794}, {384,730}, {515,12110}, {517,3398}, {519,12150}, {726,7760}, {731,904}, {944,10788}, {1078,1125}, {1385,2080}, {1386,1691}, {1428,3503}, {1482,11842}, {1582,2300}, {1698,7808}, {1829,11380}, {1837,10798}, {3057,10799}, {3097,7772}, {3576,5171}, {3579,12054}, {3616,7793}, {3624,7815}, {3640,10793}, {3641,10792}, {3734,9902}, {3751,5039}, {3795,8715}, {3972,7976}, {5034,9593}, {5182,9881}, {5252,10797}, {5315,8297}, {5587,10358}, {5657,10359}, {5886,10104}, {7987,8722}, {9798,10790}, {9857,10345}
X(12194) = orthologic center of triangle 5th anti-Brocard to these triangles: Atik, 1st circumperp, 2nd circumperp, inner-Conway, Conway, 2nd Conway, 3rd Conway, 1st Ehrmann, 3rd Euler, 4th Euler, excenters-reflections, excentral, 2nd extouch, hexyl, Honsberger, inner-Hutson, Hutson intouch, outer-Hutson, 2nd Hyacinth, intouch, inverse-in-incircle, 2nd Pamfilos-Zhou, 1st Sharygin, tangential-midarc, 2nd tangential-midarc, Yff central
X(12194) = X(1)-of-5th-anti-Brocard-triangle
X(12194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,32,11364), (1,10789,32), (8,7787,10791), (32,10800,1), (32,10803,10801), (32,10804,10802), (10789,10800,11364), (10794,10795,10796)
The reciprocal orthologic center of these triangles is X(10).
X(12195) lies on these lines: {1,83}, {6,7976}, {8,32}, {10,1078}, {98,355}, {145,7787}, {182,944}, {517,12110}, {519,12150}, {730,7760}, {760,10350}, {952,3398}, {1482,10796}, {2080,5690}, {2098,10798}, {2099,10797}, {3616,7808}, {3617,7793}, {3632,10789}, {3913,11490}, {5171,5657}, {5603,10358}, {5790,10104}, {7815,9780}, {7967,10359}, {9941,10347}, {9997,10345}, {10573,10802}, {10794,10912}, {10799,10950}, {11380,12135}
X(12195) = orthologic center of these triangles: 5th anti-Brocard to 2nd Schiffler
X(12195) = X(8)-of-5th-anti-Brocard-triangle
X(12195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10791,83), (10,11364,1078), (145,7787,10800)
The reciprocal orthologic center of these triangles is X(40).
X(12196) lies on these lines: {32,84}, {83,6260}, {98,6245}, {182,1490}, {515,12195}, {971,3398}, {1078,6705}, {1709,10801}, {5658,10359}, {6001,12194}, {6257,10793}, {6258,10792}, {6259,10796}, {7971,10800}, {7992,10789}, {9910,10790}, {10085,10802}, {11364,12114}, {11380,12136}
X(12196) = X(84)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12197) lies on these lines: {1,182}, {3,11364}, {4,10791}, {10,98}, {32,40}, {46,10802}, {65,10799}, {83,946}, {165,5171}, {172,8924}, {515,12195}, {516,12110}, {517,3398}, {962,7787}, {1078,6684}, {1385,12054}, {1699,10358}, {1836,10797}, {1902,11380}, {2080,3579}, {3097,9737}, {5034,9575}, {5119,10801}, {5603,10359}, {5812,10795}, {6361,10788}, {7808,8227}, {7982,10800}, {7991,10789}, {8669,9751}, {9911,10790}, {10306,11490}
X(12197) = reflection of X(12194) in X(3398)
X(12197) = X(40)-of-5th-anti-Brocard-triangle
X(12198) lies on these lines: {11,11364}, {32,80}, {83,214}, {100,10791}, {182,12119}, {952,12194}, {1078,6702}, {2800,12110}, {2802,12195}, {2829,12196}, {5840,12197}, {6224,7787}, {6262,10793}, {6263,10792}, {6265,10796}, {7972,10800}, {9897,10789}, {9912,10790}, {10057,10801}, {10073,10802}, {11380,12137}
X(12198) = X(80)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12199) lies on these lines: {11,98}, {32,104}, {83,119}, {100,182}, {153,7787}, {515,12198}, {952,3398}, {1078,6713}, {1317,10799}, {1768,10789}, {2783,4027}, {2787,12176}, {2800,12194}, {2802,12197}, {2829,12110}, {5039,10759}, {9913,10790}, {10058,10801}, {10074,10802}, {10698,10800}, {10742,10796}, {11364,11715}, {11380,12138}
X(12199) = X(104)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12200) lies on these lines: {32,7160}, {182,12120}, {7787,9874}, {8000,10800}, {9898,10789}, {10059,10801}, {10075,10802}, {11380,12139}
X(12200) = X(7160)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12201) lies on these lines: {30,12192}, {32,265}, {83,1511}, {98,10113}, {110,10796}, {125,2080}, {182,12121}, {2771,12198}, {3448,10788}, {5663,12110}, {10088,10797}, {10091,10798}, {11380,12140}
X(12201) = X(265)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12202) lies on these lines: {30,12193}, {32,64}, {83,2883}, {98,6247}, {182,1498}, {1078,6696}, {1503,6656}, {2080,3357}, {2777,12201}, {3398,6000}, {5171,10606}, {5656,10359}, {5878,10796}, {6001,12197}, {6225,7787}, {6266,10793}, {6267,10792}, {6759,12054}, {7355,10799}, {7973,10800}, {8567,8722}, {9899,10789}, {9914,10790}, {10060,10801}, {10076,10802}, {11380,11381}
X(12202) = X(64)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12203) lies on these lines: {2,8721}, {3,76}, {4,83}, {5,7859}, {20,32}, {30,3398}, {39,5999}, {114,7899}, {147,626}, {315,6776}, {316,2456}, {376,5171}, {382,10796}, {385,5188}, {458,1629}, {511,7470}, {515,12195}, {516,12194}, {542,7883}, {550,2080}, {631,7835}, {962,10800}, {1342,10999}, {1343,11000}, {1350,7754}, {1351,7894}, {1352,3096}, {1503,6656}, {1513,7828}, {1657,11842}, {1691,5254}, {1885,11380}, {2794,4027}, {2896,5984}, {3091,7808}, {3098,12251}, {3146,7787}, {3407,7864}, {3522,6392}, {3523,7815}, {3529,10788}, {3564,7768}, {3978,7467}, {4297,11364}, {4299,10802}, {4302,10801}, {5025,10131}, {5038,7745}, {5050,7878}, {5085,7770}, {5092,6248}, {5182,7841}, {5691,10791}, {5840,12199}, {6179,9755}, {6194,6308}, {7354,10799}, {7697,9751}, {7709,9737}, {7748,10723}, {7752,9744}, {7761,9863}, {7762,8550}, {7810,11177}, {7812,11179}, {7830,10991}, {7856,9753}, {7911,12177}, {7924,10333}, {7933,10334}, {8703,11054}, {9166,9774}, {9756,11285}, {9821,12122}, {9873,10347}, {12192,12193}
X(12203) = reflection of X(i) in X(j) for these (i,j): (12110,3398), (12195,12197)
X(12203) = X(20)-of-5th-anti-Brocard-triangle
X(12203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,98,1078), (3,11257,99), (4,182,83), (4,10359,10358), (182,10358,10359), (3398,12110,12150), (3522,7793,8722), (4027,6655,10350), (5025,10131,10352), (10358,10359,83)
The reciprocal orthologic center of these triangles is X(3).
X(12204) lies on these lines: {14,32}, {61,384}, {83,619}, {98,5469}, {182,5474}, {530,12191}, {531,11300}, {542,12201}, {617,7787}, {1078,6670}, {2080,6774}, {5182,9114}, {5613,10796}, {6269,10793}, {6271,10792}, {6773,10788}, {7974,10800}, {9900,10789}, {9915,10790}, {10061,10801}, {10077,10802}, {11364,11706}, {11380,12141}
X(12204) = X(14)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12205) lies on these lines: {13,32}, {62,384}, {83,618}, {98,5470}, {182,5473}, {530,11299}, {531,12191}, {542,12201}, {616,7787}, {1078,6669}, {2080,6771}, {5182,9116}, {5617,10796}, {6268,10793}, {6270,10792}, {6770,10788}, {7975,10800}, {9901,10789}, {9916,10790}, {10062,10801}, {11364,11705}, {11380,12142}
X(12205) = X(13)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12206) lies on these lines: {2,32}, {6,10131}, {98,6249}, {182,12122}, {194,5039}, {384,732}, {3398,7470}, {3972,6309}, {4027,5007}, {5171,9751}, {5969,7839}, {6274,10793}, {6275,10792}, {6287,9863}, {7745,9478}, {7977,10800}, {9903,10789}, {9918,10790}, {10064,10801}, {10080,10802}, {11380,12144}
X(12206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (83,1078,6704), (83,6308,2), (2896,7787,83), (10350,12150,7787)
X(12206) = X(83)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12207) lies on these lines: {32,1297}, {83,132}, {98,127}, {112,182}, {2794,4027}, {2799,12176}, {2806,12199}, {3320,10799}, {9517,12192}, {9530,12150}, {11380,12145}
X(12207) = X(1297)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12208) lies on these lines: {32,54}, {83,1209}, {98,3574}, {182,7691}, {195,11842}, {539,12150}, {1078,6689}, {1154,3398}, {2080,10610}, {2888,7787}, {6276,10793}, {6277,10792}, {6288,10796}, {7979,10800}, {9905,10789}, {9920,10790}, {10066,10801}, {10082,10802}, {10628,12192}, {11380,11576}
X(12208) = X(54)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12209) lies on these lines: {32,10266}, {11380,12146}
X(12209) = X(10266)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12210) lies on these lines: {32,486}, {83,642}, {98,6251}, {182,12123}, {487,7787}, {1078,6119}, {3564,12193}, {6280,10793}, {6281,10792}, {6290,10796}, {7980,10800}, {9906,10789}, {9921,10790}, {10067,10801}, {10083,10802}, {11380,12147}
X(12210) = X(486)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12211) lies on these lines: {32,485}, {83,641}, {98,6250}, {182,12124}, {488,7787}, {1078,6118}, {3564,12193}, {6278,10793}, {6279,10792}, {6289,10796}, {7981,10800}, {9907,10789}, {9922,10790}, {10068,10801}, {10084,10802}, {11380,12148}
X(12211) = X(485)-of-5th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12212) lies on these lines: {3,6}, {31,7077}, {69,7787}, {83,141}, {98,5306}, {110,251}, {159,10790}, {384,732}, {518,12194}, {524,6661}, {542,12201}, {611,10801}, {613,10802}, {698,7760}, {729,12074}, {755,11636}, {1078,3589}, {1184,3066}, {1352,10796}, {1353,12177}, {1386,11364}, {1469,5332}, {1501,11003}, {1503,12110}, {1613,5651}, {1843,11380}, {1992,12151}, {2211,10312}, {2781,12192}, {3056,7296}, {3124,5354}, {3242,10800}, {3329,10007}, {3407,7766}, {3416,10791}, {3564,12193}, {3618,7793}, {3751,10789}, {3763,7776}, {3972,4048}, {3981,5359}, {4027,5969}, {5031,7785}, {5103,7828}, {5182,8584}, {5846,12195}, {6179,8177}, {6308,8362}, {6636,11205}, {6776,10788}, {7837,10334}, {7893,10345}, {9225,9463}, {9830,12191}, {10358,10516}, {10359,10519}
X(12212) = reflection of X(i) in X(j) for these (i,j): (6,5007), (7768,141)
X(12212) = X(6)-of-5th-anti-Brocard-triangle
X(12212) = inverse-in-circle-{{X(371),X(372),PU(1),PU(39)}} of X(9821)
X(12212) = inverse-in-circle-{{X(1687),X(1688),PU(1),PU(2)}} of X(5092)
X(12212) = X(23)-of-X(6)PU(1)
X(12212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,32,1691), (6,1691,5038), (6,2076,39), (6,5017,3094), (32,5007,3398), (32,5039,6), (251,3051,1915), (371,372,9821), (1351,11842,182), (1687,1688,5092), (1915,3051,2056), (3094,5017,5104), (10792,10793,32)
The reciprocal orthologic center of these triangles is X(5617).
X(12213) lies on these lines: {30,12214}, {182,3642}, {298,619}, {530,12151}, {531,5182}, {533,1691}, {623,6777}, {4027,5978}, {6109,10352}, {9988,10131}
X(12213) = X(13)-of-6th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(5613).
X(12214) lies on these lines: {30,12213}, {182,3643}, {299,618}, {530,5182}, {531,12151}, {532,1691}, {624,6778}, {4027,5979}, {6108,10352}, {9989,10131}
X(12214) = X(14)-of-6th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(98).
X(12215) lies on these lines: {3,69}, {6,194}, {23,10330}, {32,6309}, {63,7019}, {76,182}, {99,511}, {110,2868}, {141,5116}, {147,325}, {183,5085}, {184,305}, {193,3552}, {315,7470}, {323,4576}, {350,1428}, {385,732}, {419,3978}, {450,6331}, {524,2076}, {525,3049}, {538,1692}, {542,5152}, {736,2458}, {1003,1992}, {1078,5092}, {1352,7763}, {1570,10754}, {1909,2330}, {2024,10352}, {2396,5967}, {2456,2782}, {3094,7783}, {3098,7782}, {3292,4563}, {3329,10334}, {3589,7797}, {3618,5286}, {3619,11285}, {3734,5034}, {3763,7945}, {3818,7752}, {3972,5039}, {5012,8024}, {5028,7781}, {5031,7925}, {5033,7751}, {5052,7816}, {5058,6318}, {5062,6314}, {5111,5969}, {5162,7813}, {5651,11059}, {6230,8294}, {6231,8293}, {7757,10000}, {7779,10997}, {7809,11645}, {9464,11003}, {9983,10131}, {10007,12055}
X(12215) = reflection of X(i) in X(j) for these (i,j): (69,6393), (385,1691), (1691,5026), (5207,325), (6393,6390), (10754,1570), (11646,5031)
X(12215) = X(1916)-of-6th-anti-Brocard-triangle
X(12215) = crosspoint of X(147) and X(194) wrt both the excentral and anticomplementary triangles
X(12215) = crossdifference of every pair of points of line X(882)X(1843)
X(12215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6,4048,384), (141,5116,7824), (193,3552,5017), (325,5989,5999), (3926,6776,69), (4027,9865,385)
The reciprocal orthologic center of these triangles is X(147).
X(12216) lies on these lines: {6,76}, {69,8150}, {182,2896}, {511,8290}, {754,2458}, {4027,9866}, {5039,10334}, {7779,10352}, {7905,12212}, {9990,10131}, {10722,12177}
X(12216) = X(11606)-of-6th-anti-Brocard-triangle
The reciprocal orthologic center of these triangles is X(6231).
X(12217) lies on these lines: {182,6229}, {642,7769}, {2462,5182}, {4027,9867}, {9991,10131}
The reciprocal orthologic center of these triangles is X(6230).
X(12218) lies on these lines: {182,6228}, {641,7769}, {2461,5182}, {4027,9868}, {9992,10131}
The reciprocal orthologic center of these triangles is X(3581).
X(12219) lies on these lines: {2,1986}, {3,3043}, {4,7723}, {20,5663}, {22,399}, {69,146}, {74,323}, {110,5562}, {113,7731}, {125,5889}, {155,3047}, {185,9706}, {265,1154}, {511,10296}, {858,10264}, {1112,3091}, {1216,11562}, {1511,10298}, {2777,12111}, {3060,7687}, {3100,7727}, {3101,7724}, {3448,11411}, {3543,12133}, {5876,7728}, {5890,6699}, {5891,11557}, {5972,11444}, {6243,10113}, {9976,11416}, {10117,11441}, {10620,11413}, {10657,11420}, {10658,11421}, {10721,12162}
X(12219) = anticomplement of X(1986)
X(12219) = orthologic center of these triangles: 1st anti-circumperp to orthocentroidal
X(12219) = X(80)-of-1st-anti-circumperp-triangle if ABC is acute
X(12219) = reflection of X(i) in X(j) for these (i,j): (4,7723), (110,5562), (5889,125), (6243,10113), (7722,3), (7728,5876), (7731,113), (10721,12162), (11562,1216), (12121,6101)
X(12219) = {X(7731), X(11459)}-harmonic conjugate of X(113)
The reciprocal orthologic center of these triangles is X(576).
X(12220) lies on these lines: {2,1843}, {3,6403}, {4,9967}, {6,22}, {20,185}, {23,1974}, {51,10565}, {66,69}, {74,3565}, {110,159}, {141,858}, {160,3001}, {182,7488}, {394,9924}, {542,12219}, {805,2697}, {1205,3448}, {1350,7691}, {1351,7592}, {1352,11444}, {1353,6243}, {1469,4296}, {1503,12111}, {1995,7716}, {2071,3098}, {2876,4329}, {3056,3100}, {3101,3779}, {3153,3818}, {3564,11412}, {3567,5050}, {3589,9971}, {3618,5640}, {3620,3917}, {3867,5133}, {4260,7520}, {5092,10298}, {5093,10263}, {5562,5921}, {6101,11898}, {6563,9009}, {6636,8541}, {7401,11387}, {8538,12088}, {8681,12058}, {10625,11411}, {11470,12087}
X(12220) = reflection of X(i) in X(j) for these (i,j): (4,9967), (69,3313), (193,6467), (1843,11574), (3448,1205), (5889,6776), (5921,5562), (6243,1353), (6403,3), (9973,141), (11898,6101)
X(12220) = anticomplement of X(1843)
X(12220) = X(7)-of-1st-anti-circumperp-triangle if ABC is acute
X(12220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69,3313,2979), (141,9973,11188), (1843,11574,2), (3618,9969,5640), (12223,12224,20)
The reciprocal orthologic center of these triangles is X(3).
X(12221) lies on these lines: {2,371}, {3,12169}, {4,193}, {8,9906}, {20,6463}, {23,9921}, {52,6239}, {69,3071}, {385,7000}, {488,6561}, {489,3053}, {490,5860}, {492,6337}, {1132,1271}, {1270,11294}, {1992,3070}, {1993,3092}, {3091,6290}, {3146,5870}, {3522,12123}, {3620,7388}, {3623,7980}, {3832,6202}, {5032,7581}, {6289,6462}, {6406,8681}, {6423,7586}, {6995,8948}, {7374,7774}, {7389,7582}, {7584,11291}
X(12221) = reflection of X(i) in X(j) for these (i,j): (8,9906), (487,486), (6281,6251), (12222,2996)
X(12221) = anticomplement of X(487)
X(12221) = {X(4),X(193)}-harmonic conjugate of X(12222)
X(12221) = orthic-to-1st-anti-circumperp similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12222) lies on these lines: {2,372}, {3,12170}, {4,193}, {8,9907}, {20,6462}, {23,9922}, {52,6400}, {69,3070}, {385,7374}, {487,6560}, {489,5861}, {490,3053}, {491,6337}, {1131,1270}, {1271,11293}, {1992,3071}, {1993,3093}, {3091,6289}, {3146,5871}, {3522,12124}, {3620,7389}, {3623,7981}, {3832,6201}, {5032,7582}, {6290,6463}, {6291,8681}, {6424,7585}, {6995,8946}, {7000,7774}, {7388,7581}, {7583,11292}
X(12222) = reflection of X(i) in X(j) for these (i,j): (8,9907), (488,485), (6278,6250), (12221,2996)
X(12222) = anticomplement of X(488)
X(12222) = {X(4),X(193)}-harmonic conjugate of X(12221)
X(12222) = orthic-to-1st-anti-circumperp similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12223) lies on these lines: {2,6291}, {3,6239}, {20,185}, {22,1151}, {489,2979}, {2071,7690}, {3060,6459}, {3100,6283}, {3101,6252}, {3565,9733}, {4296,7362}, {9974,11416}, {10667,11420}, {10668,11421}
X(12223) = reflection of X(6239) in X(3)
X(12223) = anticomplement of X(6291)
X(12223) = {X(20),X(12220)}-harmonic conjugate of X(12224)
X(12223) = X(176)-of-1st-anti-circumperp-triangle if ABC is acute
X(12223) = orthic-to-1st-anti-circumperp similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12224) lies on these lines: {2,6406}, {3,6400}, {20,185}, {22,1152}, {490,2979}, {2071,7692}, {3060,6460}, {3100,6405}, {3101,6404}, {3565,9732}, {4296,7353}, {9975,11416}, {10671,11420}, {10672,11421}
X(12224) = reflection of X(6400) in X(3)
X(12224) = anticomplement of X(6406)
X(12224) = {X(20),X(12220)}-harmonic conjugate of X(12223)
X(12224) = X(175)-of-1st-anti-circumperp-triangle if ABC is acute
X(12224) = orthic-to-1st-anti-circumperp similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4). As a point of the Euler line, X(12225) has Shinagawa coefficients: (E+2*F, -2*E-6*F).
X(12225) lies on these lines: {2,3}, {52,12022}, {343,6145}, {1141,8800}, {1503,12111}, {1568,10282}, {2697,11635}, {3070,11417}, {3071,11418}, {3100,6284}, {3101,6253}, {3164,7823}, {4296,7354}, {5254,10313}, {5318,11420}, {5321,11421}, {5523,10316}, {5596,6225}, {5640,11745}, {5654,9707}, {5889,6146}, {6247,11440}, {6696,11454}, {8550,11416}, {9820,11464}, {9833,11441}, {11064,11449}, {11457,12163}, {11459,12134}
X(12225) = reflection of X(i) in X(j) for these (i,j): (3146,1885), (5889,6146), (6240,3)
X(12225) = anticomplement of X(3575)
X(12225) = X(65)-of-1st-anti-circumperp-triangle if ABC is acute
X(12225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,7507,2), (4,20,22), (4,376,3547), (4,7404,7566), (4,7503,5133), (20,1370,11413), (20,2071,550), (20,3153,7488), (20,7396,3522), (22,858,7495), (2071,7574,858), (3153,7488,5), (3627,7403,4), (5094,7396,858), (6816,7487,1995), (7404,7566,5133), (7503,7566,7404)
The reciprocal orthologic center of these triangles is X(6243).
X(12226) lies on these lines: {2,6152}, {3,6242}, {20,1154}, {22,195}, {52,54}, {69,1225}, {74,10625}, {539,11412}, {1209,7999}, {1493,6243}, {2071,7691}, {2914,12088}, {3091,11576}, {3100,6286}, {3101,6255}, {3153,6288}, {3519,6101}, {4296,7356}, {5889,10619}, {5965,12220}, {6689,7730}, {9977,11416}, {10298,10610}, {10677,11420}, {10678,11421}, {12219,12225}
X(12226) = reflection of X(i) in X(j) for these (i,j): (3519,6101), (5889,10619), (6242,3), (6243,1493)
X(12226) = anticomplement of X(6152)
X(12226) = X(79)-of-1st-anti-circumperp-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3581).
X(12227) lies on these lines: {6,13}, {54,74}, {110,389}, {125,7592}, {155,5972}, {184,1986}, {195,12121}, {569,7723}, {578,5663}, {1112,6759}, {1147,1511}, {1181,2777}, {1994,10733}, {2904,11456}, {3043,5890}, {5012,12219}, {5609,11746}, {6467,9934}, {7724,11428}, {7727,11429}, {9306,9826}, {10620,11425}, {11402,12165}
X(12227) = orthologic center of these triangles: anti-Conway to orthocentroidal
X(12227) = {X(6), X(399)}-harmonic conjugate of X(7687)
X(12227) = X(80)-of-anti-Conway-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(10112).
X(12228) lies on these lines: {2,3043}, {3,1986}, {5,49}, {6,1511}, {26,1112}, {74,5012}, {113,184}, {125,569}, {146,11003}, {182,6699}, {389,11536}, {399,9818}, {1147,5972}, {1176,10752}, {1181,5663}, {1539,9934}, {2914,12219}, {5622,10264}, {7503,7723}, {11402,12168}, {11818,12140}
X(12228) = X(104)-of-anti-Conway-triangle if ABC is acute
X(12228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (49,567,12022), (265,11597,110), (567,11597,265)
The reciprocal orthologic center of these triangles is X(3).
X(12229) lies on these lines: {3,8908}, {182,486}, {184,487}, {642,9306}, {5012,12221}, {6290,6759}, {11402,12169}
X(12229) = orthic-to-anti-Conway similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12230) lies on these lines: {182,485}, {184,488}, {641,9306}, {3564,12229}, {5012,12222}, {6289,6759}, {11402,12170}
X(12230) = orthic-to-anti-Conway similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12231) = {3,6}, {54,6239}, {184,6291}, {485,8909}, {5012,12223}, {6252,11428}, {6283,11429}, {9306,9823}, {11402,12171}
X(12231) = {X(6),X(578)}-harmonic conjugate of X(12232)
X(12231) = X(176)-of-anti-Conway-triangle if ABC is acute
X(12231) = orthic-to-anti-Conway similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12232) lies on these lines: {3,6}, {54,6400}, {184,6406}, {5012,12224}, {6404,11428}, {6405,11429}, {9306,9824}, {11402,12172}
X(12232) = {X(6),X(578)}-harmonic conjugate of X(12231)
X(12232) = X(175)-of-anti-Conway-triangle if ABC is acute
X(12232) = orthic-to-anti-Conway similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4).
X(12233) lies on these lines: {2,9786}, {4,6}, {5,389}, {12,11436}, {20,3796}, {24,10192}, {25,11745}, {30,578}, {51,235}, {54,6240}, {64,3088}, {113,11746}, {115,8799}, {140,11438}, {141,5562}, {154,7487}, {184,3575}, {185,427}, {343,5889}, {378,5894}, {381,11432}, {382,11426}, {394,6815}, {403,3567}, {511,6823}, {524,12160}, {550,10610}, {568,10024}, {590,6810}, {615,6809}, {631,1192}, {858,10574}, {946,5173}, {1147,7706}, {1350,7400}, {1352,12164}, {1353,10112}, {1368,9729}, {1594,5890}, {1595,6000}, {1596,10110}, {1597,5878}, {1614,7576}, {1620,3524}, {1885,11424}, {1899,7507}, {1907,11381}, {3091,11433}, {3541,6696}, {3589,7395}, {3855,11431}, {3858,7687}, {4846,12085}, {5012,12225}, {5020,9815}, {5064,12174}, {5133,12111}, {5654,6642}, {5891,7405}, {6253,11428}, {6284,11429}, {6644,9820}, {6756,6759}, {6816,10601}, {6831,10478}, {7403,12162}, {7495,7691}, {7544,11441}, {9306,9825}, {9730,11585}, {11402,12173}, {11412,11660}
X(12233) = midpoint of X(4) and X(1181)
X(12233) = reflection of X(3867) in X(5480)
X(12233) = X(958)-of-orthic-triangle if ABC is acute
X(12233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,1199,12022), (4,7592,6146), (20,11427,11425), (185,427,6247), (185,3574,427), (2883,5480,4), (3541,10605,6696), (5448,5462,5), (5562,7399,141), (6146,7592,8550)
The reciprocal orthologic center of these triangles is X(6243).
X(12234) lies on these lines: {5,11536}, {6,17}, {54,186}, {184,6152}, {539,12161}, {578,1154}, {973,10274}, {1147,1493}, {1181,12173}, {1843,11808}, {1994,5562}, {2904,3574}, {5012,12226}, {6255,11428}, {6286,11429}, {6759,11576}, {7592,10619}, {7691,11430}, {8681,9972}, {9306,9827}, {10610,11438}, {11402,12175}, {11702,11746}, {12227,12233}
X(12234) = X(79)-of-anti-Conway-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(7387).
X(12235) lies on these lines: {4,52}, {6,1147}, {26,2393}, {51,155}, {143,3564}, {343,1216}, {389,10112}, {539,973}, {569,5892}, {578,9932}, {974,6146}, {1209,10170}, {1843,9908}, {3003,3133}, {3546,5447}, {3567,6193}, {5907,7687}, {5943,9820}, {6217,9930}, {6218,9929}, {7689,10606}, {9730,12118}, {9777,12166}, {9931,11436}, {9938,11438}, {10297,11692}
X(12235) = midpoint of X(52) and X(68)
X(12235) = reflection of X(i) in X(j) for these (i,j): (1147,5462), (1216,5449)
X(12235) = orthologic center of these triangles: 2nd anti-Conway to 2nd Hyacinth
X(12235) = {X(6), X(9937)}-harmonic conjugate of X(1147)
X(12235) = X(84)-of-2nd-anti-Conway-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(10112).
X(12236) lies on these lines: {4,94}, {5,11746}, {6,1511}, {30,974}, {51,113}, {52,125}, {74,3060}, {110,3567}, {389,11800}, {511,6699}, {541,11807}, {542,9969}, {567,12006}, {1154,2072}, {1216,6723}, {1353,2854}, {1493,11597}, {1994,3043}, {2071,3581}, {2777,5446}, {2781,10264}, {3047,3518}, {3548,6101}, {5462,5972}, {5889,7723}, {5890,10733}, {7530,9934}, {7731,9140}, {9777,12168}, {10111,12140}, {10114,11225}, {10263,12041}, {11262,11804}
X(12236) = midpoint of X(i) and X(j) for these {i,j}: {52,125}, {265,1986}, {389,11800}, {5446,11806}, {5889,7723}, {6102,10113}, {10111,12140}, {10263,12041}
X(12236) = reflection of X(i) in X(j) for these (i,j): (5,11746), (1112,143), (1216,6723), (1511,9826), (5972,5462)
X(12236) = 1st Droz-Farny circle-inverse-of-X(3448)
X(12236) = X(119)-of-orthic-triangle if ABC is acute
X(12236) = X(104)-of-2nd-anti-Conway-triangle if ABC is acute
X(12236) = anticenter of the cyclic quadrilateral consisting of the vertices of the orthic triangle and X(125)
X(12236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (265,568,1986), (5504,6644,1511)
The reciprocal orthologic center of these triangles is X(3).
X(12237) lies on these lines: {6,12229}, {51,487}, {486,511}, {642,5943}, {3060,12221}, {3564,5446}, {3819,6119}, {5907,6251}, {6290,10110}, {9729,12123}, {9777,12169}
X(12237) = reflection of X(i) in X(j) for these (i,j): (5907,6251), (6290,10110), (12123,9729)
X(12237) = orthic-to-2nd-anti-Conway similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12238) lies on these lines: {6,12230}, {51,488}, {485,511}, {641,5943}, {3060,12222}, {3564,5446}, {3819,6118}, {5907,6250}, {6289,10110}, {9729,12124}, {9777,12170}
X(12238) = reflection of X(i) in X(j) for these (i,j): (5907,6250), (6289,10110), (12124,9729)
X(12238) = orthic-to-2nd-anti-Conway similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12239) lies on these lines: {3,6}, {51,3071}, {155,8276}, {185,3070}, {486,5462}, {590,5562}, {1147,9682}, {1154,8981}, {1216,5418}, {1587,5890}, {1588,3567}, {2781,8991}, {3060,6459}, {3068,5889}, {5420,5892}, {5446,6561}, {5891,10576}, {5943,9823}, {5946,7584}, {6102,7583}, {6252,11435}, {6283,11436}, {6457,8577}, {6460,10574}, {6564,12162}, {8252,11695}, {8253,11793}, {9540,11412}, {9683,9687}, {9777,12171}
X(12239) = {X(6),X(389)}-harmonic conjugate of X(12240)
X(12239) = X(176)-of-2nd-anti-Conway-triangle if ABC is acute
X(12239) = orthic-to-2nd-anti-Conway similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12240) lies on these lines: {3,6}, {51,3070}, {155,8277}, {185,3071}, {485,5462}, {615,5562}, {1216,5420}, {1587,3567}, {1588,5890}, {3060,6460}, {3069,5889}, {5418,5892}, {5446,6560}, {5891,10577}, {5943,9824}, {5946,7583}, {6102,7584}, {6404,11435}, {6405,11436}, {6458,8576}, {6459,10574}, {6565,12162}, {8252,11793}, {8253,11695}, {8981,12006}, {8998,9826}, {9777,12172}
X(12240) = {X(6),X(389)}-harmonic conjugate of X(12239)
X(12240) = X(175)-of-2nd-anti-Conway-triangle if ABC is acute
X(12240) = orthic-to-2nd-anti-Conway similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4).
Let A'B'C' be the midheight triangle. Let AB, AC be the orthogonal projections of A' on CA, AB, resp. Define BC, BA, CA, CB cyclically. Let A" = CAAC∩ABBA, and define B" nad C" cyclically. Triangle A"B"C" is homothetic to ABC at X(6). X(12241) = X(4)-of-A"B"C". (Randy Hutson, March 29, 2020)
X(12241) lies on these lines: {2,11425}, {4,6}, {5,578}, {12,11429}, {20,9786}, {30,143}, {51,3575}, {54,403}, {68,9818}, {140,11430}, {141,7395}, {154,3089}, {182,6823}, {184,235}, {185,1885}, {230,1970}, {265,5576}, {343,7503}, {376,1192}, {378,6696}, {381,11426}, {382,11432}, {394,6816}, {427,11424}, {524,5562}, {550,11438}, {567,10024}, {590,6809}, {615,6810}, {1211,7549}, {1352,11479}, {1495,10619}, {1593,1899}, {1596,6759}, {1598,9833}, {1620,3528}, {1746,6831}, {1853,3088}, {1907,11550}, {3060,12225}, {3091,11427}, {3542,10192}, {3564,5907}, {3567,6240}, {3589,7399}, {3629,12160}, {3850,7687}, {5085,7400}, {5462,9826}, {5894,10605}, {5943,9825}, {6253,11435}, {6284,11436}, {6523,6618}, {6642,12118}, {6756,10110}, {6815,10601}, {7553,11750}, {7576,9781}, {9777,12173}
X(12241) = midpoint of X(i) and X(j) for these {i,j}: {4,6146}, {185,1885}, {5907,10112}, {7553,11750}
X(12241) = reflection of X(i) in X(j) for these (i,j): (3575,11745), (6756,10110), (12024,12022)
X(12241) = X(960)-of-orthic-triangle if ABC is acute
X(12241) = X(65)-of-2nd-anti-Conway-triangle if ABC is acute
X(12241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,6,12233), (4,1181,2883), (4,6776,1498), (4,10982,5480), (4,12022,6146), (20,11433,9786), (51,3575,11745), (397,398,1990), (1587,1588,1249), (1593,1899,6247), (1885,11245,185), (2883,8550,1181), (3070,3071,53)
The reciprocal orthologic center of these triangles is X(6243).
Let A'B'C' be the reflection triangle. Let Oa be the circle centered at A' and tangent to BC, and define Ob, Oc cyclically. X(12242) is the radical center of circles Oa, Ob, Oc. (Randy Hutson, July 21, 2017)
Let A'B'C' be the medial triangle. Let Ba and Ca be the orthogonal projections of B' and C' on line BC, resp. Let (Oa) be the circle with segment BaCa as diameter. Define (Ob) and (Oc) cyclically. X(12242) is the radical center of circles (Oa), (Ob), (Oc). (Randy Hutson, November 2, 2017)
X(12242) lies on these lines: {2,11431}, {4,54}, {5,539}, {6,17}, {51,6152}, {125,1199}, {140,389}, {397,6116}, {398,6117}, {468,973}, {542,5576}, {550,10610}, {575,11585}, {576,3549}, {974,10628}, {1487,7604}, {1657,11425}, {2888,5056}, {2917,3517}, {3060,12226}, {3090,11271}, {3523,7691}, {3567,6242}, {3628,10275}, {3850,7687}, {3851,6288}, {4857,11429}, {5449,11225}, {5462,5972}, {5476,7529}, {5943,9820}, {6217,6276}, {6218,6277}, {6255,11435}, {6286,11436}, {9777,12175}, {9813,9972}, {9905,11522}, {9969,11808}, {10110,11576}, {10114,11702}, {11064,11695}
X(12242) = midpoint of X(i) and X(j) for these {i,j}: {4,10619}, {5,1493}, {54,3574}, {125,2914}, {140,11803}, {195,1209}, {11576,11577}, {11702,11804}
X(12242) = reflection of X(i) in X(j) for these (i,j): (6689,8254), (11576,10110)
X(12242) = trilinear pole, wrt half-altitude triangle, of orthic axis
X(12242) = X(3647)-of-orthic-triangle if ABC is acute
X(12242) = X(79)-of-2nd-anti-Conway-triangle if ABC is acute
X(12242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,54,10619), (6,195,12234), (17,18,233), (195,1656,3519), (1656,3519,1209), (3574,10619,4), (8254,11803,140)
The reciprocal orthologic center of these triangles is X(9855).
X(12243) lies on these lines: {2,2782}, {3,7616}, {4,542}, {20,8596}, {24,9876}, {30,148}, {40,2796}, {76,9302}, {98,376}, {99,3524}, {110,11656}, {114,5071}, {115,3545}, {147,381}, {338,5648}, {388,10054}, {497,10070}, {511,11054}, {515,9875}, {530,6773}, {531,6770}, {631,2482}, {3090,5461}, {3455,7556}, {3528,10992}, {3529,10991}, {3543,5984}, {3564,8352}, {3839,6033}, {5182,10359}, {5286,6034}, {5523,6761}, {5657,9881}, {6248,7827}, {6776,7620}, {7487,12132}, {7615,9744}, {7790,11178}, {7967,9884}, {8550,10488}, {9755,11159}, {9882,10783}, {9883,10784}, {9890,11257}, {10053,10385}, {10304,12042}, {10788,12191}, {11179,11185}, {11180,11646}
X(12243) = midpoint of X(i) and X(j) for these {i,j}: {20,8596}, {148,11177}, {3543,5984}
X(12243) = reflection of X(i) in X(j) for these (i,j): (2,11632), (4,671), (99,6055), (110,11656), (147,381), (376,98), (2482,11623), (3543,6321), (6054,115), (8591,3), (9862,11177), (10488,8550), (11177,12188), (11180,11646)
X(12243) = anticomplement of X(8724)
X(12243) = orthologic center of these triangles: anti-Euler to McCay
X(12243) = X(671)-of-anti-Euler-triangle
X(12243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (99,6055,3524), (114,9166,5071), (115,6054,3545), (148,12188,9862)
The reciprocal orthologic center of these triangles is X(12112).
X(12244) lies on these lines: {2,7728}, {3,146}, {4,74}, {20,5663}, {24,9919}, {30,3448}, {67,11738}, {110,376}, {113,631}, {185,7731}, {186,10117}, {265,3146}, {382,10264}, {388,10065}, {399,550}, {477,1138}, {497,10081}, {515,9904}, {542,11001}, {690,9862}, {974,11431}, {1181,2914}, {1511,3522}, {1539,3091}, {2771,9961}, {2781,6776}, {2931,12088}, {2935,3520}, {3028,4294}, {3060,11806}, {3090,6699}, {3431,10293}, {3524,5972}, {3529,11411}, {3534,9143}, {3543,10113}, {3567,11807}, {3830,11801}, {4299,7727}, {5071,6723}, {5480,5621}, {5603,11709}, {5655,10304}, {6225,9934}, {6241,10628}, {7487,12133}, {7505,11270}, {7552,11454}, {7577,10606}, {7725,10783}, {7726,10784}, {7967,7978}, {10295,12112}, {10323,12168}, {10574,11557}, {10788,12192}
X(12244) = reflection of X(i) in X(j) for these (i,j): (4,74), (74,10990), (146,3), (382,10264), (399,550), (2935,5894), (3146,265), (3448,10620), (6225,9934), (7728,12041), (7731,185), (9143,3534), (10721,125), (12112,10295)
X(12244) = anticomplement of X(7728)
X(12244) = X(74)-of-anti-Euler-triangle
X(12244) = orthologic center of these triangles: anti-Euler to orthocentroidal
X(12244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (74,10721,125), (125,10721,4), (7728,12041,2)
The reciprocal orthologic center of these triangles is X(10).
X(12245) lies on these lines: {1,631}, {2,1482}, {3,145}, {4,8}, {5,3617}, {7,7317}, {10,3090}, {20,952}, {21,10679}, {40,376}, {46,3476}, {55,6875}, {65,1056}, {78,6927}, {80,5225}, {100,6942}, {104,5854}, {140,3622}, {149,6928}, {165,3633}, {239,7397}, {390,5729}, {404,10680}, {443,10597}, {495,6937}, {496,6963}, {497,5697}, {498,11009}, {515,3529}, {516,3625}, {528,11827}, {529,11826}, {758,12115}, {920,3486}, {938,9957}, {946,3545}, {953,6079}, {956,6906}, {960,6898}, {999,6940}, {1006,3295}, {1058,3057}, {1075,3176}, {1125,3533}, {1145,5730}, {1159,11036}, {1210,7962}, {1317,5204}, {1320,6891}, {1350,9053}, {1385,3241}, {1389,6852}, {1512,6736}, {1697,3488}, {1698,11224}, {1699,4668}, {1766,5839}, {2077,8666}, {2093,10106}, {2095,6904}, {2098,3086}, {2099,3085}, {2550,6901}, {2551,3878}, {2800,5904}, {2802,6903}, {2886,6874}, {2975,6950}, {3088,11396}, {3091,4678}, {3149,8158}, {3242,10519}, {3244,3576}, {3245,4299}, {3296,5559}, {3340,3487}, {3428,3913}, {3485,8164}, {3523,3623}, {3525,3616}, {3526,10283}, {3528,3579}, {3544,9955}, {3600,6955}, {3626,3855}, {3634,9624}, {3635,10164}, {3656,5071}, {3661,7402}, {3817,4691}, {3820,6975}, {3868,6916}, {3876,6939}, {3877,5084}, {3880,6899}, {3885,6865}, {3889,10202}, {3893,7957}, {3940,6848}, {4004,9776}, {4007,10445}, {4189,11849}, {4293,10944}, {4294,10950}, {4295,5252}, {4311,5128}, {4323,11374}, {4345,5704}, {4511,6880}, {4677,5691}, {4816,9589}, {4853,6769}, {4861,6977}, {5044,5804}, {5067,5734}, {5087,7704}, {5126,6049}, {5288,5450}, {5289,8256}, {5550,11231}, {5552,6949}, {5601,11253}, {5602,11252}, {5604,10518}, {5605,10517}, {5656,7973}, {5658,7971}, {5687,6905}, {5714,9578}, {5722,9785}, {5727,10624}, {5759,5853}, {5761,6856}, {5763,6844}, {5768,6764}, {5789,6847}, {5836,6854}, {5837,9623}, {5846,6776}, {6734,6956}, {6735,6969}, {6743,6766}, {6825,10528}, {6873,7680}, {6883,12000}, {6896,7686}, {6920,9708}, {6932,10942}, {6943,10943}, {6946,9709}, {6952,10527}, {6989,10587}, {7487,12135}, {7512,8193}, {7709,7976}, {8128,11924}, {8192,10323}, {8715,11012}, {9669,11545}, {9798,12088}, {9997,10357}, {10175,11522}, {10359,10800}, {10588,11280}, {10785,10912}, {10788,12195}, {11822,11844}, {11823,11843}
X(12245) = midpoint of X(i) and X(j) for these {i,j}: {20,3621}, {3632,7991}, {3893,7957}
X(12245) = reflection of X(i) in X(j) for these (i,j): (1,11362), (4,8), (145,3), (944,40), (962,355), (1482,5690), (3241,3654), (3529,6361), (3633,5882), (4301,3626), (5881,3625), (6361,7991), (7982,10), (8148,5), (10698,1145), (11531,946)
X(12245) = anticomplement of X(1482)
X(12245) = orthologic center of these triangles: anti-Euler to 2nd Schiffler
X(12245) = X(8)-of-anti-Euler-triangle
X(12245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5657,631), (1,9588,10165), (1,11362,5657), (2,1482,10595), (3,145,7967), (8,962,355), (8,3869,3421), (8,11415,5176), (10,5603,3090), (10,7982,5603), (40,944,376), (100,11249,6942), (140,10247,3622), (165,3633,5882), (355,962,4), (1482,5690,2), (3419,5758,4), (5080,10525,4), (5175,5812,4), (5697,10573,497)
The reciprocal orthologic center of these triangles is X(40).
Let A'B'C' be the Hutson-extouch triangle. Let La be the tangent to the A-excircle at A', and define B' and C' cyclically. Let A" = Lb∩Lc, B" = Lc∩La, C" = La∩Lb. Triangle A"B"C" is homothetic to ABC at X(57), and X(12246) = X(4)-of-A"B"C". (Randy Hutson, July 21, 2017)
X(12246) lies on these lines: {1,7955}, {2,6259}, {3,5658}, {4,57}, {20,72}, {24,9910}, {30,9799}, {104,10309}, {376,1490}, {388,1709}, {443,3358}, {452,10167}, {497,10085}, {515,3529}, {516,6762}, {631,5316}, {944,3057}, {946,4355}, {1012,3487}, {1158,5657}, {1768,1788}, {2801,3189}, {2829,6253}, {3090,6705}, {3146,5787}, {3304,3649}, {3427,10308}, {3474,4848}, {3600,9856}, {3982,11522}, {4297,5698}, {4298,11372}, {5129,11227}, {5259,5450}, {5714,6847}, {5815,6244}, {5818,6256}, {5927,6904}, {6257,10784}, {6258,10783}, {6865,7171}, {6868,9960}, {6872,11220}, {6916,7330}, {6936,9942}, {7487,12136}, {7704,10785}, {7967,7971}, {10788,12196}, {10884,11111}
X(12246) = reflection of X(i) in X(j) for these (i,j): (4,84), (3146,5787), (5691,9948)
X(12246) = anticomplement of X(6259)
X(12246) = X(84)-of-anti-Euler-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12247) lies on these lines: {1,6952}, {2,6265}, {3,8}, {4,80}, {10,6326}, {11,2099}, {24,9912}, {119,2476}, {145,6972}, {149,517}, {153,355}, {214,631}, {376,12119}, {377,9964}, {388,10044}, {443,9946}, {484,515}, {497,10051}, {519,6264}, {528,5759}, {912,5176}, {938,1387}, {962,10738}, {1056,5083}, {1320,6943}, {1389,6831}, {1478,11571}, {1482,1484}, {1532,11545}, {1537,12019}, {1788,10090}, {2550,2801}, {2802,6903}, {2829,6253}, {2949,5541}, {3036,6937}, {3090,6702}, {3476,10074}, {3485,8068}, {3486,10058}, {3617,10786}, {3632,7993}, {3679,5531}, {3754,6901}, {3878,6902}, {4214,12138}, {5218,7967}, {5289,6963}, {5790,11698}, {5805,6797}, {5840,6361}, {6262,10784}, {6263,10783}, {6906,10950}, {7487,12137}, {9809,10742}, {9963,10993}, {10788,12198}
X(12247) = midpoint of X(i) and X(j) for these {i,j}: {8,9803}, {1768,9897}, {3632,7993}
X(12247) = reflection of X(i) in X(j) for these (i,j): (1,10265), (4,80), (153,355), (944,104), (962,10738), (1482,1484), (1532,11545), (1537,12019), (5541,11362), (6224,3), (6326,10), (7967,11219), (7972,11715), (9809,10742), (9963,10993), (10698,11)
X(12247) = anticomplement of X(6265)
X(12247) = X(80)-of-anti-Euler-triangle
X(12247) = X(6326)-of-outer-Garcia-triangle
X(12247) = inner-Garcia-to-outer-Garcia similarity image of X(4)
X(12247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11,10698,5603), (7972,11219,11715), (7972,11715,7967)
The reciprocal orthologic center of these triangles is X(40).
X(12248) lies on the cubic K542 and these lines: {2,10742}, {3,153}, {4,11}, {20,952}, {24,9913}, {30,149}, {80,1788}, {100,376}, {119,631}, {382,1484}, {388,10058}, {390,6938}, {484,515}, {495,6906}, {497,10074}, {516,6264}, {528,11001}, {944,2800}, {1317,4294}, {1387,3600}, {1537,6147}, {2096,11041}, {2771,3648}, {2787,9862}, {2801,5759}, {2802,6361}, {2828,5667}, {3035,3524}, {3090,6713}, {3146,10738}, {3486,11570}, {3488,5083}, {3529,5840}, {4297,6326}, {4996,6876}, {5071,6667}, {5218,6950}, {5225,5533}, {5229,8068}, {5450,6952}, {5603,11715}, {5691,10265}, {5731,6265}, {6256,6949}, {6845,9655}, {6930,11729}, {6965,10269}, {7487,12138}, {10788,12199}
X(12248) = reflection of X(i) in X(j) for these (i,j): (4,104), (153,3), (382,1484), (3146,10738), (5691,10265), (6326,4297), (9809,6265), (10728,11), (12247,1768)
X(12248) = anticomplement of X(10742)
X(12248) = X(104)-of-anti-Euler-triangle
X(12248) = Cundy-Parry Phi transform of X(3563)
X(12248) = Cundy-Parry Psi transform of X(3564)
X(12248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11,10728,4), (104,10728,11), (5731,9809,6265)
The reciprocal orthologic center of these triangles is X(40).
X(12249) lies on these lines: {3,9874}, {4,1697}, {376,12120}, {388,10059}, {497,10075}, {515,9898}, {944,7957}, {2951,6361}, {5759,7674}, {7487,12139}, {7967,8000}, {10788,12200}
X(12249) = reflection of X(i) in X(j) for these (i,j): (4,7160), (9874,3)
X(12249) = X(7160)-of-anti-Euler-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12250) lies on these lines: {2,3357}, {3,5656}, {4,64}, {20,2979}, {24,9914}, {30,11411}, {74,3542}, {154,3528}, {376,1498}, {388,10060}, {497,10076}, {515,9899}, {550,11206}, {631,2883}, {1204,3089}, {1294,3346}, {1503,3529}, {1515,6616}, {2777,3146}, {3088,3574}, {3090,6696}, {3091,7703}, {3426,6756}, {3522,6759}, {3524,8567}, {3545,5893}, {3566,5489}, {3962,6001}, {4293,6285}, {4294,7355}, {4846,7404}, {5663,6193}, {5890,11431}, {6145,11738}, {6241,6776}, {6266,10784}, {6267,10783}, {7401,11472}, {7487,11381}, {7967,7973}, {10192,10299}, {10282,10304}, {10788,12202}
X(12250) = reflection of X(i) in X(j) for these (i,j): (4,64), (1498,5894), (3529,5925), (5878,3357), (5895,6247), (6225,3)
X(12250) = anticomplement of X(5878)
X(12250) = X(64)-of-anti-Euler-triangle
X(12250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,6225,5656), (1498,5894,376), (2883,10606,631), (3357,5878,2), (5895,6247,4)
The reciprocal orthologic center of these triangles is X(3).
X(12251) lies on these lines: {2,3095}, {3,194}, {4,69}, {5,3314}, {6,10359}, {20,2782}, {24,9917}, {30,9863}, {39,631}, {40,726}, {83,576}, {98,7751}, {99,5171}, {114,7796}, {140,7806}, {182,7760}, {262,3090}, {343,5117}, {376,538}, {384,10788}, {388,10063}, {394,419}, {497,10079}, {515,9902}, {575,7894}, {698,1350}, {730,944}, {732,6776}, {1078,9737}, {1351,7770}, {1513,3933}, {1569,5206}, {1656,7931}, {1975,11676}, {2080,3552}, {2794,7826}, {3068,3103}, {3069,3102}, {3091,7697}, {3094,5286}, {3097,6684}, {3398,7766}, {3523,11171}, {3524,7757}, {3525,7786}, {3533,6683}, {3545,9466}, {3734,12110}, {3926,5976}, {5097,7878}, {5969,12243}, {6272,10784}, {6273,10783}, {7487,12143}, {7758,8149}, {7781,8722}, {7795,9753}, {7802,9991}, {7967,7976}, {10333,10796}, {10983,11285}
X(12251) = reflection of X(i) in X(j) for these (i,j): (4,76), (20,9821), (194,3), (7709,6194), (7758,8149), (11257,5188)
X(12251) = anticomplement of X(3095)
X(12251) = X(76)-of-anti-Euler-triangle
X(12251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,194,7709), (194,6194,3), (262,3934,3090), (5188,11257,376), (9821,9983,9862)
The reciprocal orthologic center of these triangles is X(3).
X(12252) lies on these lines: {2,6287}, {3,147}, {4,83}, {20,3095}, {24,9918}, {98,8150}, {376,754}, {382,7864}, {388,10064}, {497,10080}, {515,9903}, {546,7923}, {550,7762}, {631,6292}, {732,6776}, {3090,6704}, {3528,6337}, {3529,7737}, {3796,5117}, {5569,9774}, {6274,10784}, {6275,10783}, {6655,10131}, {7487,12144}, {7791,10334}, {7869,10299}, {7967,7977}, {10788,12206}, {11001,12156}
X(12252) = reflection of X(i) in X(j) for these (i,j): (4,83), (20,8725), (2896,3)
X(12252) = anticomplement of X(6287)
X(12252) = X(83)-of-anti-Euler-triangle
X(12252) = X(6292), X(9751)}-harmonic conjugate of X(631)
The reciprocal orthologic center of these triangles is X(4).
X(12253) lies on these lines: {4,127}, {112,376}, {132,631}, {2781,5596}, {2794,3529}, {2799,9862}, {2806,12248}, {3146,10749}, {3320,4294}, {3524,6720}, {4293,6020}, {7487,12145}, {9517,12244}, {10788,12207}, {11641,12082}
X(12253) = reflection of X(i) in X(j) for these (i,j): (4,1297), (3146,10749)
X(12253) = X(1297)-of-anti-Euler-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12254) lies on these lines: {2,6288}, {3,2888}, {4,54}, {20,1154}, {24,9920}, {30,195}, {49,3153}, {156,11597}, {186,2917}, {265,5944}, {376,539}, {381,8254}, {388,10066}, {389,7730}, {497,10082}, {515,9905}, {631,1209}, {973,11431}, {1141,3459}, {1199,3575}, {1493,3146}, {1511,11565}, {1568,9705}, {1885,12112}, {2914,5895}, {3060,10115}, {3090,6689}, {3431,6145}, {3518,12022}, {3519,3522}, {3520,6247}, {3567,11808}, {3581,11264}, {4299,7356}, {4302,6286}, {5073,11803}, {6153,9730}, {6241,10628}, {6242,6776}, {6276,10784}, {6277,10783}, {7487,11576}, {7552,9927}, {7728,11702}, {7967,7979}, {9862,9985}, {9977,11179}, {10574,11802}, {10788,12208}, {11464,11704}, {11577,12250}
X(12254) = reflection of X(i) in X(j) for these (i,j): (4,54), (54,10619), (2888,3), (6288,10610), (7728,11702)
X(12254) = anticomplement of X(6288)
X(12254) = X(54)-of-anti-Euler-triangle
X(12254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54,1614,10274), (6288,10610,2)
The reciprocal orthologic center of these triangles is X(79).
X(12255) lies on these lines: {4,5885}, {5330,12248}, {7487,12146}, {10788,12209}
X(12255) = reflection of X(4) in X(10266)
X(12255) = X(10266)-of-anti-Euler-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12256) lies on these lines: {2,6290}, {3,69}, {4,372}, {20,6463}, {24,9921}, {98,638}, {147,8317}, {182,11292}, {184,1589}, {193,9732}, {376,5860}, {388,10067}, {485,7612}, {497,10083}, {515,9906}, {615,8406}, {631,642}, {637,9991}, {1151,8550}, {1152,1503}, {1181,1578}, {1352,11291}, {1587,6423}, {1588,6421}, {1590,1899}, {3090,6119}, {3102,6459}, {3155,11433}, {3156,11206}, {3592,12007}, {3594,5480}, {5408,7386}, {5871,6813}, {5965,7692}, {6215,11316}, {7374,9748}, {7487,12147}, {7494,11090}, {7967,7980}, {9862,9986}, {9863,11293}, {10788,12210}, {10984,12229}
X(12256) = midpoint of X(i) and X(j) for these {i,j}: {20,12221}, {6280,12123}
X(12256) = reflection of X(i) in X(j) for these (i,j): (4,486), (487,3), (6281,642)
X(12256) = anticomplement of X(6290)
X(12256) = X(486)-of-anti-Euler-triangle
X(12256) = {X(3),X(6776)}-harmonic conjugate of X(12257)
The reciprocal orthologic center of these triangles is X(3).
X(12257) lies on these lines: {2,6222}, {3,69}, {4,371}, {20,6462}, {24,9922}, {98,637}, {147,8316}, {182,11291}, {184,1590}, {193,9733}, {376,5861}, {388,10068}, {486,7612}, {497,10084}, {515,9907}, {590,8414}, {631,641}, {638,9992}, {1151,1503}, {1152,8550}, {1181,1579}, {1352,11292}, {1587,6422}, {1588,6424}, {1589,1899}, {3069,8911}, {3090,6118}, {3103,6460}, {3155,11206}, {3156,11433}, {3592,5480}, {3594,12007}, {5409,7386}, {5870,6811}, {5871,9541}, {5965,7690}, {6214,11315}, {7000,9748}, {7487,12148}, {7494,11091}, {7967,7981}, {9862,9987}, {9863,11294}, {10788,12211}, {10984,12230}
X(12257) = midpoint of X(i) and X(j) for these {i,j}: {20,12222}, {6279,12124}
X(12257) = reflection of X(i) in X(j) for these (i,j): (4,485), (488,3), (6278,641)
X(12257) = anticomplement of X(6289)
X(12257) = X(485)-of-anti-Euler-triangle
X(12257) = {X(3),X(6776)}-harmonic conjugate of X(12256)
The reciprocal orthologic center of these triangles is X(9855).
X(12258) lies on these lines: {1,671}, {2,9881}, {10,5461}, {30,11710}, {115,519}, {350,1111}, {515,9880}, {530,11706}, {531,11705}, {542,946}, {543,551}, {1086,1125}, {1386,9830}, {3027,4870}, {3545,9864}, {3576,12117}, {3616,8591}, {3622,8596}, {3655,6321}, {3656,11632}, {3679,7983}, {4301,11623}, {5184,8859}, {5603,12243}, {5886,8724}, {9876,11365}, {9878,11368}, {9882,11370}, {9883,11371}, {11363,12132}, {11364,12191}
X(12258) = midpoint of X(i) and X(j) for these {i,j}: {1,671}, {551,11599}, {3655,6321}, {3656,11632}, {3679,7983}, {9875,9884}
X(12258) = reflection of X(i) in X(j) for these (i,j): (10,5461), (551,11725), (2482,1125), (11711,551)
X(12258) = complement of X(9881)
X(12258) = X(671)-of-anti-Aquila-triangle
X(12258) = orthologic center of these triangles: anti-Aquila to McCay
X(12258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9875,9884), (671,9884,9875), (7983,9166,3679), (11599,11725,11711)
The reciprocal orthologic center of these triangles is X(9833).
X(12259) lies on these lines: {1,68}, {2,9928}, {5,226}, {10,5449}, {155,5886}, {515,9927}, {516,7689}, {539,551}, {1069,11376}, {1125,1147}, {1386,3564}, {3157,11375}, {3576,12118}, {3616,6193}, {3817,5448}, {4297,11709}, {5603,11411}, {5654,8227}, {7352,12047}, {9624,9936}, {9820,11230}, {9908,11365}, {9923,11368}, {9929,11370}, {9930,11371}, {10165,12038}, {11363,12134}, {11364,12193}
X(12259) = midpoint of X(i) and X(j) for these {i,j}: {1,68}, {9896,9933}
X(12259) = reflection of X(i) in X(j) for these (i,j): (10,5449), (1147,1125)
X(12259) = complement of X(9928)
X(12259) = X(68)-of-anti-Aquila-triangle
X(12259) = orthologic center of these triangles: anti-Aquila to 2nd Hyacinth
The reciprocal orthologic center of these triangles is X(40).
X(12260) lies on these lines: {1,5920}, {3,5542}, {10,6767}, {11,1058}, {55,3487}, {200,3646}, {405,4533}, {946,3295}, {954,1490}, {1001,3811}, {1125,6600}, {3576,12120}, {3616,9874}, {3913,10198}, {5603,12249}, {5763,10267}, {6147,11495}, {6743,11108}, {11363,12139}, {11364,12200}
X(12260) = midpoint of X(i) and X(j) for these {i,j}: {1,7160}, {8000,9898}
X(12260) = X(7160)-of-anti-Aquila-triangle
X(12260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9898,8000), (7160,8000,9898)
The reciprocal orthologic center of these triangles is X(6102).
X(12261) lies on these lines: {1,265}, {11,113}, {30,11709}, {110,5886}, {125,517}, {355,7984}, {515,10113}, {516,12041}, {542,1386}, {946,5663}, {952,11801}, {1125,1511}, {1385,11735}, {1699,7728}, {1836,10081}, {2807,11806}, {2948,8227}, {3448,5603}, {3576,12121}, {3579,6699}, {3656,7978}, {5901,11720}, {5972,11230}, {6265,10778}, {6723,11231}, {9812,12244}, {10088,11375}, {10091,11376}, {11363,12140}, {11364,12201}
X(12261) = midpoint of X(i) and X(j) for these {i,j}: {1,265}, {355,7984}, {3656,9140}, {6265,10778}
X(12261) = reflection of X(i) in X(j) for these (i,j): (113,9955), (1385,11735), (1511,1125), (3579,6699), (11699,11723), (11720,5901)
X(12261) = X(265)-of-anti-Aquila-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12262) lies on these lines: {1,64}, {3,960}, {10,6696}, {30,12259}, {40,10606}, {57,1854}, {65,4219}, {154,7987}, {165,8567}, {221,3601}, {515,6247}, {516,5894}, {517,3357}, {912,12084}, {1125,2883}, {1192,7713}, {1204,1829}, {1319,6285}, {1385,6000}, {1420,2192}, {1498,3576}, {1503,4297}, {1699,5895}, {1853,5691}, {2646,7355}, {2777,12261}, {3616,6225}, {3817,5893}, {5603,12250}, {5878,5886}, {6266,11371}, {6267,11370}, {7520,9961}, {9914,11365}, {11363,11381}, {11364,12202}
X(12262) = midpoint of X(i) and X(j) for these {i,j}: {1,64}, {7973,9899}
X(12262) = reflection of X(i) in X(j) for these (i,j): (10,6696), (2883,1125
X(12262) = X(64)-of-anti-Aquila-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12263) lies on these lines: {1,76}, {10,3934}, {37,39}, {194,3616}, {262,8227}, {355,7697}, {384,11364}, {385,12194}, {511,946}, {515,6248}, {516,5188}, {519,9466}, {538,551}, {731,9063}, {732,1386}, {962,6194}, {1269,1964}, {1385,2782}, {2140,3836}, {3095,5886}, {3097,3624}, {3576,11257}, {4093,4647}, {5603,12251}, {5969,12258}, {6179,10789}, {6272,11371}, {6273,11370}, {7751,10800}, {7770,10791}, {9917,11365}, {9983,11368}, {11230,11272}, {11363,12143}
X(12263) = midpoint of X(i) and X(j) for these {i,j}: {1,76}, {7976,9902}
X(12263) = reflection of X(i) in X(j) for these (i,j): (10,3934), (39,1125)
X(12263) = X(76)-of-anti-Aquila-triangle
X(12263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9902,7976), (76,7976,9902), (3097,3624,7786)
The reciprocal orthologic center of these triangles is X(3).
X(12264) lies on these lines: {1,83}, {10,6704}, {40,9751}, {515,6249}, {551,754}, {732,1386}, {1125,1279}, {2896,3616}, {3576,12122}, {5603,12252}, {5886,6287}, {5901,11710}, {6274,11371}, {6275,11370}, {8150,10800}, {9918,11365}, {11363,12144}, {11364,12206}
X(12264) = midpoint of X(i) and X(j) for these {i,j}: {1,83}, {7977,9903}
X(12264) = reflection of X(i) in X(j) for these (i,j): (10,6704), (6292,1125)
X(12264) = X(83)-of-anti-Aquila-triangle
X(12264) = X(3)-of-1st-Hyacinth-triangle
X(12264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9903,7977), (83,7977,9903)
The reciprocal orthologic center of these triangles is X(4).
X(12265) lies on these lines: {1,1297}, {40,10705}, {112,3576}, {127,515}, {132,1125}, {214,2831}, {551,9530}, {1319,6020}, {1385,11722}, {2646,3320}, {2781,11720}, {2794,4297}, {2799,11710}, {2806,11715}, {2825,11712}, {2853,11713}, {5603,12253}, {6720,10165}, {9517,11709}, {9518,11714}, {9523,11716}, {9527,11717}, {9532,11700}, {10780,12119}, {11363,12145}, {11364,12207}
X(12265) = midpoint of X(i) and X(j) for these {i,j}: {1,1297}, {40,10705}, {10780,12119}
X(12265) = reflection of X(i) in X(j) for these (i,j): (132,1125), (11722,1385)
X(12265) = X(1297)-of-anti-Aquila-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12266) lies on these lines: {1,54}, {10,6689}, {195,10246}, {515,3574}, {517,10610}, {539,551}, {952,8254}, {960,1493}, {1125,1209}, {1154,1385}, {2888,3616}, {3576,7691}, {5603,12254}, {5882,12242}, {5886,6288}, {5901,11720}, {6276,11371}, {6277,11370}, {9920,11365}, {9985,11368}, {10628,11709}, {11363,11576}, {11364,12208}
X(12266) = midpoint of X(i) and X(j) for these {i,j}: {1,54}, {7979,9905}
X(12266) = reflection of X(i) in X(j) for these (i,j): (10,6689), (1209,1125)
X(12266) = X(54)-of-anti-Aquila-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12267) lies on these lines: {1,5180}, {11,11263}, {5603,12255}, {11363,12146}, {11364,12209}
X(12267) = midpoint of X(1) and X(10266)
X(12267) = X(10266)-of-anti-Aquila-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12268) lies on these lines: {1,486}, {10,6119}, {56,481}, {487,3616}, {515,6251}, {642,1125}, {1386,3564}, {3576,12123}, {3622,12221}, {5603,12256}, {5886,6290}, {6280,11371}, {6281,9624}, {9921,11365}, {9986,11368}, {11363,12147}, {11364,12210}
X(12268) = midpoint of X(1) and X(486)
X(12268) = reflection of X(642) in X(1125)
X(12268) = X(486)-of-anti-Aquila-triangle
X(12268) = {X(1386),X(5901)}-harmonic conjugate of X(12269)
The reciprocal orthologic center of these triangles is X(3).
X(12269) lies on these lines: {1,485}, {10,6118}, {56,482}, {488,3616}, {515,6250}, {641,1125}, {1386,3564}, {3576,12124}, {3622,12222}, {5603,12257}, {5886,6289}, {6278,9624}, {6279,11370}, {9922,11365}, {9987,11368}, {11363,12148}, {11364,12211}
X(12269) = midpoint of X(1) and X(485)
X(12269) = reflection of X(641) in X(1125)
X(12269) = X(485)-of-anti-Aquila-triangle
X(12269) = {X(1386),X(5901)}-harmonic conjugate of X(12268)
Orthologic centers: X(12270)-X(12431)
Centers X(12270)-X(12431) were contributed by César Eliud Lozada, March 16, 2017.
The reciprocal orthologic center of these triangles is X(3581).
X(12270) lies on these lines: {3,74}, {4,11557}, {20,10628}, {30,7731}, {113,7577}, {125,10574}, {146,1531}, {185,3448}, {265,5890}, {381,11561}, {974,9140}, {1176,5621}, {1539,11455}, {1986,3060}, {1993,12165}, {2781,12220}, {2979,12219}, {3543,11807}, {3567,10113}, {4846,11442}, {5640,7687}, {5889,7722}, {6143,12162}, {7547,11439}, {7724,11445}, {7727,11446}, {9826,11451}, {9976,11443}, {10575,12244}, {10657,11452}, {10658,11453}, {11412,12121}, {11422,12227}
X(12270) = reflection of X(i) in X(j) for these (i,j): (4,11562), (3448,185), (5889,7722), (10733,1986), (11412,12121), (12111,110), (12244,10575)
X(12270) = orthologic center of these triangles: 3rd anti-Euler to orthocentroidal
X(12270) = X(80)-of-3rd-anti-Euler-triangle if ABC is acute
X(12270) = {X(1986), X(10733)}-harmonic conjugate of X(3060)
The reciprocal orthologic center of these triangles is X(7387).
X(12271) lies on these lines: {68,11444}, {110,9937}, {155,3060}, {1147,1199}, {1993,12166}, {2979,11411}, {3167,3567}, {3564,11412}, {5562,8681}, {5640,12235}, {5889,6193}, {6391,7395}, {6403,12160}, {9820,11451}, {9926,11443}, {9931,11446}, {9932,11449}, {9938,11454}, {10659,11452}, {10660,11453}
X(12271) = reflection of X(5889) in X(6193)
X(12271) = X(84)-of-3rd-anti-Euler-triangle if ABC is acute
X(12271) = orthologic center of these triangles: 3rd anti-Euler to 2nd Hyacinth
The reciprocal orthologic center of these triangles is X(576).
X(12272) lies on these lines: {2,6467}, {4,12271}, {6,110}, {22,9924}, {25,6391}, {52,11387}, {66,69}, {157,4558}, {182,11449}, {193,1843}, {489,12224}, {490,12223}, {511,3146}, {524,9973}, {542,12270}, {1350,11440}, {1351,5198}, {1353,3567}, {1992,9969}, {1993,12167}, {3056,11446}, {3098,11454}, {3564,3575}, {3620,7998}, {3629,9971}, {3630,8705}, {3779,11445}, {5093,9781}, {5157,8542}, {5181,6697}, {6515,11382}, {6776,10574}, {9027,11008}, {9822,11451}, {9967,11444}, {10733,12133}, {11412,11898}
X(12272) = reflection of X(i) in X(j) for these (i,j): (193,1843), (5889,6403), (11412,11898), (12111,5921), (12220,69)
X(12272) = anticomplement of X(6467)
X(12272) = X(7)-of-3rd-anti-Euler-triangle if ABC is acute
X(12272) = {X(12276),X(12277)}-harmonic conjugate of X(12111)
X(12272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69,12220,2979), (193,1843,3060), (3620,11574,7998)
The reciprocal orthologic center of these triangles is X(10112).
X(12273) lies on these lines: {24,110}, {74,2979}, {113,3060}, {125,11444}, {146,511}, {265,11459}, {399,1154}, {542,12219}, {568,10272}, {631,11806}, {1511,5890}, {1657,5663}, {1993,12168}, {2781,9924}, {3091,11800}, {3448,5562}, {5640,12236}, {6101,10620}, {6241,12121}, {6699,7998}, {9833,10628}, {10625,12244}, {10663,11452}, {10664,11453}, {10733,12133}, {11422,12228}
X(12273) = reflection of X(i) in X(j) for these (i,j): (3448,5562), (5889,110), (6241,12121), (7731,399), (10620,6101), (12244,10625)
X(12273) = X(104)-of-3rd-anti-Euler-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3).
X(12274) lies on these lines: {486,7998}, {487,3060}, {642,11451}, {2979,12221}, {3564,12275}, {5640,12237}, {11422,12229}
X(12274) = orthic-to-3rd-anti-Euler similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12275) lies on these lines: {485,7998}, {488,3060}, {641,11451}, {1993,12170}, {2979,12222}, {3564,12274}, {5640,12238}, {11422,12230}
X(12275) = orthic-to-3rd-anti-Euler similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12276) lies on these lines: {110,1151}, {489,2979}, {511,3146}, {1993,12171}, {3060,6291}, {5640,12239}, {5889,6239}, {6252,11445}, {6283,11446}, {7690,11454}, {9823,11451}, {9974,11443}, {10667,11452}, {10668,11453}, {11422,12231}
X(12276) = reflection of X(5889) in X(6239)
X(12276) = {X(12111),X(12272)}-harmonic conjugate of X(12277)
X(12276) = X(176)-of-3rd-anti-Euler-triangle if ABC is acute
X(12276) = orthic-to-3rd-anti-Euler similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12277) lies on these lines: {110,1152}, {490,2979}, {511,3146}, {1993,12172}, {3060,6406}, {5640,12240}, {5889,6400}, {6404,11445}, {6405,11446}, {7692,11454}, {9824,11451}, {9975,11443}, {10671,11452}, {10672,11453}, {11422,12232}
X(12277) = reflection of X(5889) in X(6400)
X(12277) = {X(12111),X(12272)}-harmonic conjugate of X(12276)
X(12277) = X(175)-of-3rd-anti-Euler-triangle if ABC is acute
X(12277) = orthic-to-3rd-anti-Euler similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4).
X(12278) lies on these lines: {4,110}, {5,11449}, {20,2888}, {24,9938}, {30,11412}, {186,9927}, {376,11750}, {382,11441}, {550,11454}, {1092,3153}, {1199,7706}, {1204,3448}, {1503,12272}, {1511,10255}, {1885,11439}, {1993,12173}, {2979,12225}, {3060,3575}, {3070,11447}, {3071,11448}, {5059,5921}, {5318,11452}, {5321,11453}, {5640,12241}, {5889,6240}, {6146,10574}, {6253,11445}, {6284,11446}, {7526,8907}, {7577,12038}, {8550,11443}, {9825,11451}, {10024,11464}, {10619,11003}, {11250,12121}, {11422,12233}, {11550,12086}
X(12278) = reflection of X(5889) in X(6240)
X(12278) = X(65)-of-3rd-anti-Euler-triangle if ABC is acute
X(12278) = {X(20), X(11442)}-harmonic conjugate of X(11440)
The reciprocal orthologic center of these triangles is X(389).
X(12279) lies on these lines: {30,5889}, {110,1498}, {143,382}, {184,12086}, {185,3060}, {373,3854}, {376,5447}, {389,3543}, {511,5059}, {548,7999}, {550,11459}, {858,2883}, {1147,7464}, {1181,11422}, {1370,6225}, {1425,9539}, {1499,11450}, {1503,12272}, {1593,5012}, {1614,12084}, {1657,5663}, {1658,11468}, {1993,12174}, {2071,6759}, {2777,12270}, {2918,10323}, {3091,11695}, {3100,7355}, {3357,7488}, {3426,7395}, {3516,6800}, {3522,5907}, {3528,5891}, {3529,12271}, {3534,5876}, {3567,3627}, {3830,9781}, {3832,9729}, {3850,11465}, {3855,5892}, {4296,6285}, {5073,6102}, {5076,5946}, {5422,11403}, {6254,11445}, {7509,11472}, {7527,10984}, {7689,12088}, {7691,9920}, {8549,11443}, {10170,10299}, {10304,11793}, {10539,12112}, {10625,11001}, {10675,11452}, {10676,11453}, {11250,11464}, {11456,12085}, {12082,12163}
X(12279) = reflection of X(i) in X(j) for these (i,j): (4,10575), (3146,185), (5073,6102), (5889,6241), (11412,1657), (12111,20)
X(12279) = anticomplement of X(11381)
X(12279) = X(8)-of-3rd-anti-Euler-triangle if ABC is acute
X(12279) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,11381,11439), (4,10574,5640), (20,12111,2979), (185,3146,3060), (376,12162,11444), (1498,11413,110), (2071,6759,11449), (3357,7488,11454), (3522,5907,7998), (3832,9729,11451)
The reciprocal orthologic center of these triangles is X(6243).
X(12280) lies on these lines: {4,12273}, {52,11271}, {54,6644}, {110,143}, {155,3060}, {382,1154}, {539,5889}, {1350,7691}, {1493,3567}, {1595,11664}, {1993,12175}, {2888,3153}, {2914,10539}, {2979,12226}, {3519,11412}, {5640,12242}, {5965,12272}, {6255,11445}, {6286,11446}, {9827,11451}, {9977,11443}, {10574,10619}, {10677,11452}, {10678,11453}, {11422,12234}, {12270,12278}
X(12280) = reflection of X(i) in X(j) for these (i,j): (5889,6242), (11271,52), (11412,3519)
X(12280) = X(79)-of-3rd-anti-Euler-triangle if ABC is acute
X(12281) lies on these lines: {2,11562}, {3,74}, {4,7730}, {125,5890}, {146,12162}, {185,6143}, {265,5889}, {568,11801}, {578,2914}, {1539,11439}, {1656,11561}, {1986,3567}, {2781,6403}, {2918,8718}, {2979,12121}, {3060,10113}, {3091,11557}, {3153,3448}, {6000,12244}, {7592,12165}, {7687,9781}, {7724,11460}, {7727,11461}, {9826,11465}, {9976,11458}, {10224,10264}, {10657,11466}, {10658,11467}, {11412,12219}, {11423,12227}
X(12281) = reflection of X(i) in X(j) for these (i,j): (110,7723), (146,12162), (399,5876), (5889,265), (6241,74), (7722,125), (7731,4), (11412,12219), (12270,3)
X(12281) = anticomplement of X(11562)
X(12281) = X(80)-of-4th-anti-Euler-triangle if ABC is acute
X(12281) = orthologic center of these triangles: 4th anti-Euler to orthocentroidal
X(12281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,7723,11459), (125,7722,5890), (6241,11459,11464)
The reciprocal orthologic center of these triangles is X(7387).
X(12282) lies on these lines: {3,12271}, {52,6995}, {68,11459}, {155,1995}, {185,8681}, {1147,11423}, {1370,11411}, {1593,6391}, {1614,9937}, {3060,5198}, {3564,3575}, {5890,6193}, {7592,12166}, {9781,12235}, {9820,11465}, {9926,11458}, {9931,11461}, {9932,11464}, {9938,11468}, {10659,11466}, {10660,11467}
X(12282) = reflection of X(i) in X(j) for these (i,j): (11412,11411), (12271,3)
X(12282) = orthologic center of these triangles: 4th anti-Euler to 2nd Hyacinth
X(12282) = X(84)-of-4th-anti-Euler-triangle if ABC is acute
X(12282) = {X(5889), X(12272)}-harmonic conjugate of X(3575)
The reciprocal orthologic center of these triangles is X(576).
X(12283) lies on these lines: {3,12272}, {4,6467}, {6,1173}, {20,2013}, {24,9924}, {69,11457}, {74,1296}, {154,11746}, {182,11188}, {511,3529}, {542,12281}, {1351,11456}, {1353,3060}, {1843,3567}, {2393,5890}, {2979,11898}, {3056,11461}, {3098,11468}, {3564,11412}, {3779,11460}, {5050,9707}, {5921,9967}, {6391,11414}, {7592,12167}, {7998,10300}, {7999,11574}, {8550,9973}, {9822,11465}, {9971,12007}, {11387,11432}
X(12283) = reflection of X(i) in X(j) for these (i,j): (4,6467), (5921,9967), (6403,6776), (9973,8550), (11412,12220), (12272,3)
X(12283) = X(7)-of-4th-anti-Euler-triangle if ABC is acute
X(12283) = {X(12287),X(12288)}-harmonic conjugate of X(6241)
X(12283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5921,9967,11459), (6403,6776,5890)
The reciprocal orthologic center of these triangles is X(10112).
X(12284) lies on these lines: {2,11806}, {3,12273}, {4,11800}, {52,146}, {74,9938}, {110,5890}, {113,3567}, {125,11459}, {265,12111}, {382,5663}, {399,6102}, {511,12244}, {542,6403}, {1112,10706}, {1154,10620}, {1511,9704}, {1614,2931}, {1986,10594}, {2979,12041}, {3047,11464}, {3060,7728}, {3153,3448}, {6699,7999}, {7592,12168}, {7723,9140}, {9781,12236}, {10663,11466}, {10664,11467}, {11423,12228}, {12270,12278}
X(12284) = reflection of X(i) in X(j) for these (i,j): (146,52), (399,6102), (7731,5889), (11412,74), (12111,265), (12273,3), (12281,3448)
X(12284) = X(104)-of-4th-anti-Euler-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3).
X(12285) lies on these lines: {3,12274}, {486,7999}, {487,3567}, {642,11465}, {3564,12286}, {7592,12169}, {9781,12237}, {11412,12221}, {11423,12229}
X(12285) = orthic-to-4th-anti-Euler similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12286) lies on these lines: {3,12275}, {485,7999}, {488,3567}, {641,11465}, {3564,12285}, {7592,12170}, {9781,12238}, {11412,12222}, {11423,12230}
X(12286) = orthic-to-4th-anti-Euler similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12287) lies on these lines: {3,12276}, {511,3529}, {1151,1614}, {3567,6291}, {5890,6239}, {6252,11460}, {6283,11461}, {7592,12171}, {7690,11468}, {9781,12239}, {9823,11465}, {9974,11458}, {10667,11466}, {10668,11467}, {11412,12223}, {11423,12231}
X(12287) = {X(6241),X(12283)}-harmonic conjugate of X(12288)
X(12287) = X(176)-of-4th-anti-Euler-triangle if ABC is acute
X(12287) = orthic-to-4th-anti-Euler similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12288) lies on these lines: {3,12277}, {511,3529}, {1152,1614}, {3567,6406}, {5890,6400}, {6404,11460}, {6405,11461}, {7592,12172}, {7692,11468}, {9781,12240}, {9824,11465}, {9975,11458}, {10671,11466}, {10672,11467}, {11412,12224}, {11423,12232}
X(12288) = {X(6241),X(12283)}-harmonic conjugate of X(12287)
X(12288) = X(175)-of-4th-anti-Euler-triangle if ABC is acute
X(12288) = orthic-to-4th-anti-Euler similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4).
X(12289) lies on these lines: {3,12278}, {4,54}, {5,10546}, {20,68}, {30,5889}, {185,12063}, {265,1658}, {381,9707}, {382,11456}, {550,11468}, {1147,3153}, {1503,12283}, {1885,11455}, {2072,11449}, {3070,11462}, {3071,11463}, {3567,3575}, {3583,9638}, {3627,11422}, {5073,12174}, {5318,11466}, {5321,11467}, {5448,9544}, {5449,10298}, {5654,9705}, {5878,10721}, {5890,6146}, {5944,10254}, {6253,11460}, {6284,11461}, {6293,7731}, {6776,8537}, {7488,9927}, {7576,9781}, {7592,12173}, {8550,11458}, {9825,11465}, {9932,11413}, {10018,11704}, {11270,11564}, {11412,12225}, {11423,12233}, {11430,11572}, {12273,12281}
X(12289) = reflection of X(i) in X(j) for these (i,j): (20,11750), (6240,6146), (11412,12225), (12278,3)
X(12289) = X(65)-of-4th-anti-Euler-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(389).
X(12290) lies on these lines: {30,11412}, {52,3543}, {54,1593}, {110,12084}, {143,5076}, {186,3357}, {376,5907}, {378,1498}, {381,10574}, {382,5663}, {403,6247}, {477,6080}, {548,7998}, {550,11444}, {568,3853}, {1092,7464}, {1147,12086}, {1154,5073}, {1181,11423}, {1204,3518}, {1503,12283}, {1514,7729}, {1594,2883}, {1597,7592}, {1656,11017}, {1657,2979}, {1658,11454}, {1870,6285}, {1907,10938}, {2013,3146}, {2071,10539}, {2777,12281}, {3060,3627}, {3090,10219}, {3516,9707}, {3520,6759}, {3522,5891}, {3528,11793}, {3529,5562}, {3534,11591}, {3541,5656}, {3544,11695}, {3545,9729}, {3830,6102}, {3832,9730}, {3839,5462}, {3843,5640}, {3850,11451}, {4846,7544}, {5059,10625}, {5068,5892}, {5072,12046}, {5870,12288}, {5871,12287}, {5894,10295}, {5895,6152}, {6198,7355}, {6254,11460}, {6696,10018}, {7503,11472}, {7691,12083}, {7728,12270}, {8549,11458}, {10540,11250}, {10594,10605}, {10675,11466}, {10676,11467}, {11270,11738}, {11441,12085}
X(12290) = reflection of X(i) in X(j) for these (i,j): (4,11381), (20,12162), (1657,5876), (3529,5562), (5059,10625), (5889,382), (5890,11455), (6241,4), (7731,10721), (11412,12111), (12270,7728), (12279,3), (12284,10733)
X(12290) = anticomplement of X(10575)
X(12290) = X(8)-of-4th-anti-Euler-triangle if ABC is acute
X(12290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,185,3567), (4,5890,9781), (4,6241,5890), (4,11381,11455), (20,12162,11459), (185,3567,5890), (186,3357,11468), (376,5907,7999), (378,1498,1614), (1593,11456,54), (1597,12174,7592), (1657,5876,2979), (1870,6285,11461), (3520,6759,11464), (3520,12112,6759), (3545,9729,11465), (3567,6241,185), (6241,11455,4), (10540,11250,11449)
The reciprocal orthologic center of these triangles is X(6243).
X(12291) lies on these lines: {3,12280}, {6,24}, {20,12284}, {185,12254}, {195,1614}, {511,11271}, {539,11412}, {1154,1657}, {1205,11457}, {1216,2888}, {1493,3060}, {2013,12163}, {2914,6759}, {2979,3519}, {5890,6242}, {5965,12283}, {6255,11460}, {6286,11461}, {7592,12175}, {7691,11468}, {9781,12242}, {9827,11465}, {9977,11458}, {10677,11466}, {10678,11467}, {11423,12234}, {12273,12281}
X(12291) = reflection of X(i) in X(j) for these (i,j): (6152,11577), (6242,10619), (11412,12226), (12280,3)
X(12291) = X(79)-of-4th-anti-Euler-triangle if ABC is acute
X(12291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54,6152,3567), (3567,6152,7730), (6152,11577,54)
X(12292) lies on these lines: {4,94}, {24,64}, {25,10620}, {30,7723}, {34,7727}, {70,11744}, {110,378}, {113,1594}, {125,403}, {185,7687}, {186,12041}, {235,10264}, {399,1593}, {541,7576}, {974,6241}, {1511,3520}, {1902,2771}, {1905,11670}, {2777,6240}, {2781,6403}, {3028,6198}, {3043,5609}, {3091,9826}, {3146,12219}, {5504,11441}, {5890,11746}, {6152,10628}, {6699,10018}, {7547,11439}, {7724,11471}, {9976,11470}, {10151,11801}, {10657,11475}, {10658,11476}, {10733,12111}, {11403,12165}, {11424,12227}
X(12292) = midpoint of X(i) and X(j) for these {i,j}: {74,12290}, {3146,12219}, {10721,12281}, {10733,12111}
X(12292) = reflection of X(i) in X(j) for these (i,j): (4,12133), (185,7687), (1986,4), (6240,12140), (6241,974), (7722,1112), (10575,6699)
X(12292) = polar circle-inverse-of-X(7728)
X(12292) = orthologic center of these triangles: anti-excenters-reflections to orthocentroidal
X(12292) = X(80)-of-anti-excenters-reflections-triangle if ABC is acute
X(12292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,7722,1112), (1112,7722,1986), (11455,12281,10721)
The reciprocal orthologic center of these triangles is X(7387).
X(12293) lies on these lines: {3,125}, {4,155}, {5,11425}, {22,12289}, {24,9938}, {30,64}, {34,9931}, {52,12173}, {70,12225}, {185,12235}, {378,9932}, {381,1147}, {382,6243}, {539,3830}, {546,5654}, {912,3901}, {1069,3583}, {1593,9937}, {1656,12038}, {1657,7689}, {1853,12084}, {1885,11472}, {2013,11455}, {3091,9820}, {3146,11411}, {3157,3585}, {3167,3843}, {3564,3627}, {3853,9936}, {5504,10113}, {5663,5895}, {6284,10055}, {6564,8909}, {6800,12254}, {7354,10071}, {7706,11432}, {9926,11470}, {10659,11475}, {10660,11476}, {10733,12111}, {11403,12166}, {11414,11750}, {11439,12271}
X(12293) = midpoint of X(3146) and X(11411)
X(12293) = reflection of X(i) in X(j) for these (i,j): (3,9927), (155,4), (185,12235), (1657,7689), (5504,10113), (12118,5), (12163,68)
X(12293) = orthologic center of these triangles: anti-excenters-reflections to 2nd Hyacinth
X(12293) = X(84)-of-anti-excenters-reflections-triangle if ABC is acute
X(12293) = {X(3167), X(3843)}-harmonic conjugate of X(5448)
The reciprocal orthologic center of these triangles is X(576).
X(12294) lies on these lines: {2,12058}, {3,1974}, {4,69}, {6,64}, {20,11574}, {24,3098}, {25,1350}, {30,9967}, {33,1469}, {34,3056}, {39,2211}, {51,125}, {52,1595}, {141,235}, {182,378}, {184,1619}, {193,11469}, {232,3094}, {373,5094}, {389,3088}, {468,5650}, {518,1902}, {542,12292}, {1205,2777}, {1216,1598}, {1351,1597}, {1353,5095}, {1503,1885}, {1596,5891}, {1907,3867}, {2063,9306}, {2807,3751}, {2854,12133}, {2979,6995}, {3060,7378}, {3089,10519}, {3091,9822}, {3146,12220}, {3313,3575}, {3516,5085}, {3517,5447}, {3520,5092}, {3564,12162}, {3618,9729}, {3619,6622}, {3779,11471}, {3819,6353}, {4219,4260}, {4232,7998}, {5017,10311}, {5097,7722}, {5104,10985}, {5198,7716}, {5921,8681}, {5943,8889}, {5969,12131}, {6000,6776}, {6756,10625}, {7507,9969}, {7715,10627}, {9024,12138}, {10628,10752}, {11403,11477}, {11439,12272}, {11455,12283}
X(12294) = midpoint of X(i) and X(j) for these {i,j}: {193,12111}, {3146,12220}, {6467,11381}
X(12294) = reflection of X(i) in X(j) for these (i,j): (20,11574), (69,5907), (185,6), (1843,4)
X(12294) = X(7)-of-anti-excenters-reflections-triangle if ABC is acute
X(12294) = X(20)-of-1st-orthosymmedial-triangle
X(12294) = {X(12298),X(12299)}-harmonic conjugate of X(4)
The reciprocal orthologic center of these triangles is X(10112).
X(12295) lies on these lines: {3,6723}, {4,110}, {20,6699}, {30,125}, {52,3627}, {64,265}, {74,3146}, {115,2420}, {185,12236}, {381,5972}, {399,5076}, {511,7723}, {541,3448}, {542,1351}, {546,1511}, {974,10575}, {1112,11562}, {1539,3853}, {1593,2931}, {1699,11723}, {1986,5446}, {3060,7722}, {3818,5181}, {3839,11693}, {3845,5642}, {3861,10272}, {5449,11454}, {5609,12102}, {6000,11800}, {6564,8998}, {7978,9812}, {9140,12244}, {9730,11746}, {9880,11656}, {10264,10990}, {10297,10564}, {10663,11475}, {10664,11476}, {10723,11005}, {10728,10778}, {11403,12168}, {11424,12228}, {11439,12273}, {11455,12284}, {12133,12162}
X(12295) = midpoint of X(i) and X(j) for these {i,j}: {4,10733}, {74,3146}, {265,382}, {3448,10721}, {10723,11005}, {10728,10778}
X(12295) = reflection of X(i) in X(j) for these (i,j): (3,7687), (20,6699), (113,4), (125,10113), (185,12236), (1511,546), (1539,3853), (1986,5446), (5181,3818), (5642,3845), (10272,3861), (10564,10297), (10575,974), (10990,10264), (11562,1112), (11656,9880), (11693,3839), (12041,11801), (12121,5972), (12162,12133)
X(12295) = anticomplement of X(38726)
X(12295) = X(10698)-of-orthic-triangle if ABC is acute
X(12295) = X(104)-of-anti-excenters-reflections-triangle if ABC is acute
X(12295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381,12121,5972), (3448,3543,10721), (10113,12041,11801), (11801,12041,125)
The reciprocal orthologic center of these triangles is X(3).
X(12296) lies on these lines: {2,6251}, {4,487}, {20,486}, {30,12256}, {148,5871}, {185,12237}, {382,3564}, {488,6231}, {516,9906}, {642,3091}, {3071,8406}, {3146,5870}, {3523,6119}, {4293,10083}, {4294,10067}, {5731,12268}, {6459,8375}, {11403,12169}, {11424,12229}, {11439,12274}, {11455,12285}
X(12296) = midpoint of X(3146) and X(12221)
X(12296) = reflection of X(i) in X(j) for these (i,j): (20,486), (185,12237), (487,4), (12123,6251)
X(12296) = anticomplement of X(12123)
X(12296) = orthic-to-anti-excenters-reflections similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12297) lies on these lines: {2,6250}, {4,488}, {20,485}, {30,12257}, {148,5870}, {185,12238}, {382,3564}, {487,6230}, {516,9907}, {641,3091}, {671,8982}, {3070,8414}, {3146,5871}, {3523,6118}, {4293,10084}, {4294,10068}, {5731,12269}, {6460,8376}, {11403,12170}, {11424,12230}, {11439,12275}, {11455,12286}
X(12297) = midpoint of X(3146) and X(12222)
X(12297) = reflection of X(i) in X(j) for these (i,j): (20,485), (185,12238), (488,4), (12124,6250)
X(12297) = anticomplement of X(12124)
X(12297) = orthic-to-anti-excenters-reflections similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12298) lies on these lines: {4,69}, {24,7690}, {33,7362}, {34,6283}, {185,3070}, {1151,1593}, {1160,8948}, {3091,9823}, {3092,9974}, {3146,12223}, {6252,11471}, {10311,11474}, {10667,11475}, {10668,11476}, {11403,12171}, {11424,12231}, {11439,12276}, {11455,12287}
X(12298) = midpoint of X(3146) and X(12223)
X(12298) = reflection of X(i) in X(j) for these (i,j): (185,12239), (6291,4)
X(12298) = {X(4),X(12294)}-harmonic conjugate of X(12299)
X(12298) = X(176)-of-anti-excenters-reflections-triangle if ABC is acute
X(12298) = orthic-to-anti-excenters-reflections similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12299) lies on these lines: {4,69}, {24,7692}, {33,7353}, {34,6405}, {185,3071}, {1152,1593}, {1161,8946}, {3091,9824}, {3093,9975}, {3146,12224}, {6404,11471}, {10311,11473}, {10671,11475}, {10672,11476}, {11403,12172}, {11424,12232}, {11439,12277}, {11455,12288}
X(12299) = midpoint of X(3146) and X(12224)
X(12299) = reflection of X(i) in X(j) for these (i,j): (185,12240), (6406,4)
X(12299) = {X(4),X(12294)}-harmonic conjugate of X(12298)
X(12299) = X(175)-of-anti-excenters-reflections-triangle if ABC is acute
X(12299) = orthic-to-anti-excenters-reflections similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(6243).
X(12300) lies on these lines: {4,93}, {24,7691}, {33,7356}, {34,6286}, {54,64}, {125,389}, {185,12242}, {195,1593}, {403,1209}, {539,12162}, {546,7723}, {973,7547}, {1493,2914}, {1885,12292}, {2904,11426}, {3091,9827}, {3146,12226}, {3518,11591}, {3520,10610}, {3541,10937}, {5562,7576}, {5965,12294}, {6000,10619}, {6240,10625}, {6255,11471}, {7730,11743}, {9977,11470}, {10594,11459}, {10677,11475}, {10678,11476}, {11271,11469}, {11403,12175}, {11424,12234}, {11439,12280}, {11455,12291}, {11472,12111}, {11577,12290}
X(12300) = midpoint of X(3146) and X(12226)
X(12300) = reflection of X(i) in X(j) for these (i,j): (185,12242), (6152,4), (6242,11576)
X(12300) = X(79)-of-anti-excenters-reflections-triangle if ABC is acute
X(12300) = {X(4), X(6242)}-harmonic conjugate of X(11576)
The reciprocal orthologic center of these triangles is X(7387).
X(12301) lies on these lines: {3,68}, {25,12293}, {30,9908}, {56,9931}, {64,12085}, {74,2013}, {155,1593}, {378,6193}, {1147,9818}, {1350,7689}, {3516,12166}, {3564,12084}, {5646,7393}, {6642,9927}, {7387,10117}, {7503,11487}, {9786,12235}, {9820,11479}, {9926,11477}, {10625,12163}, {10659,11480}, {10660,11481}, {11411,11413}, {11440,12271}
X(12301) = reflection of X(i) in X(j) for these (i,j): (3,9938), (9937,3), (11477,9926)
X(12301) = X(84)-of-anti-Hutson-intouch-triangle if ABC is acute
X(12301) = orthologic center of these triangles: anti-Hutson intouch to 2nd Hyacinth
The reciprocal orthologic center of these triangles is X(10112).
X(12302) lies on these lines: {3,125}, {24,10733}, {25,12295}, {30,10117}, {64,155}, {68,10264}, {74,9938}, {110,378}, {113,1593}, {146,12086}, {394,7723}, {399,1147}, {1069,7727}, {1350,5621}, {1511,7526}, {1993,7722}, {2071,3448}, {2771,9928}, {2777,9914}, {3047,11456}, {3516,12168}, {5646,7514}, {5972,9818}, {6642,7687}, {6644,10113}, {7464,12244}, {9786,12236}, {9908,10990}, {10663,11480}, {10664,11481}, {11250,12118}, {11425,12228}, {11438,11800}, {11440,12273}
X(12302) = reflection of X(i) in X(j) for these (i,j): (68,10264), (155,5504), (399,1147), (2931,3), (2935,12084), (12163,74), (12293,265)
X(12302) = X(104)-of-anti-Hutson-intouch-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3).
X(12303) lies on these lines: {3,486}, {25,12296}, {74,12285}, {487,1593}, {642,11479}, {1597,6290}, {3516,12169}, {3564,12085}, {5020,6251}, {9786,12237}, {11413,12221}, {11425,12229}, {11440,12274}
X(12303) = orthic-to-anti-Hutson-intouch similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12304) lies on these lines: {3,485}, {25,12297}, {74,12286}, {488,1593}, {641,11479}, {1597,6289}, {3516,12170}, {3564,12085}, {5020,6250}, {9786,12238}, {11413,12222}, {11425,12230}, {11440,12275}
X(12304) = orthic-to-anti-Hutson-intouch similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12305) lies on these lines: {3,6}, {20,492}, {22,5406}, {25,12298}, {30,6289}, {55,7362}, {56,6283}, {74,12287}, {154,5408}, {325,490}, {378,6239}, {488,1503}, {524,12257}, {548,12123}, {1593,6291}, {1853,11090}, {2979,5407}, {3516,12171}, {5480,11292}, {5584,6252}, {6312,6399}, {6813,7778}, {8982,9766}, {9823,11479}, {11413,12223}, {11440,12276}
X(12305) = {X(3),X(1350)}-harmonic conjugate of X(12306)
X(12305) = X(176)-of-anti-Hutson-intouch-triangle if ABC is acute
X(12305) = orthic-to-anti-Hutson-intouch similarity image of X(6291)
X(12305) = reflection of X(i) in X(j) for these (i,j): (3,7690), (1151,3), (11477,9974)
The reciprocal orthologic center of these triangles is X(3).
X(12306) lies on these lines: {3,6}, {20,491}, {22,5407}, {25,12299}, {30,6290}, {55,7353}, {56,6405}, {74,12288}, {154,5409}, {325,489}, {376,1991}, {378,6400}, {487,1503}, {524,12256}, {548,12124}, {1593,6406}, {1853,11091}, {2979,5406}, {3516,12172}, {5480,11291}, {5584,6404}, {6222,6316}, {6811,7778}, {9824,11479}, {11413,12224}, {11440,12277}
X(12306) = reflection of X(i) in X(j) for these (i,j): (3,7692), (1152,3)
X(12306) = {X(3),X(1350)}-harmonic conjugate of X(12305)
X(12306) = X(175)-of-anti-Hutson-intouch-triangle if ABC is acute
X(12306) = orthic-to-anti-Hutson-intouch similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(6243).
X(12307) lies on these lines: {3,54}, {5,7693}, {20,10620}, {25,12300}, {30,2888}, {55,7356}, {56,6286}, {64,1657}, {74,12291}, {378,6242}, {381,1209}, {382,6288}, {399,2917}, {539,3534}, {548,11271}, {550,12254}, {568,11802}, {631,8254}, {973,3527}, {1092,11597}, {1216,3581}, {1350,5965}, {1593,6152}, {1597,11576}, {1656,3574}, {2070,5562}, {3516,12175}, {3523,11803}, {3526,5646}, {3579,9905}, {5054,6689}, {5584,6255}, {5663,5898}, {5876,5899}, {6243,11424}, {7666,10274}, {7689,12302}, {7730,10263}, {7979,8148}, {9786,12242}, {9827,11479}, {9914,9920}, {9977,11477}, {10605,10619}, {10677,11480}, {10678,11481}, {11413,12226}, {11425,12234}, {11440,12280}
X(12307) = reflection of X(i) in X(j) for these (i,j): (3,7691), (195,3), (382,6288), (8148,7979), (9905,3579), (11477,9977), (12254,550)
X(12307) = X(79)-of-anti-Hutson-intouch-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3581).
X(12308) lies on these lines: {3,74}, {4,11703}, {25,7722}, {113,3851}, {125,5055}, {146,382}, {265,3527}, {378,11935}, {381,3448}, {541,11820}, {542,1351}, {567,12162}, {1482,2771}, {1498,5898}, {1597,12292}, {1598,1986}, {1656,10264}, {3028,7373}, {3043,3516}, {3066,11806}, {3167,12302}, {3295,7727}, {3303,6126}, {3304,7343}, {3526,10272}, {3534,9143}, {5070,6053}, {5073,12164}, {5093,9970}, {5169,11804}, {6407,10819}, {6408,10820}, {7687,11432}, {7724,10306}, {9704,11559}, {9826,11484}, {9976,11482}, {10113,10706}, {10145,10817}, {10146,10818}, {10246,11699}, {10657,11485}, {10658,11486}, {10733,12160}, {11414,12219}, {11426,12227}
X(12308) = reflection of X(i) in X(j) for these (i,j): (3,399), (74,5609), (382,146), (3534,9143), (9919,1498), (10620,110)
X(12308) = Stammler circle-inverse-of-X(110)
X(12308) = orthologic center of these triangles: anti-incircle-circles to orthocentroidal
X(12308) = X(80)-of-anti-incircle-circles-triangle if ABC is acute
X(12308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,10620,3), (399,10620,110)
The reciprocal orthologic center of these triangles is X(7387).
X(12309) lies on these lines: {3,68}, {4,12166}, {25,6193}, {155,1351}, {159,10243}, {539,9908}, {567,5544}, {1147,5020}, {1597,12293}, {2013,11456}, {3167,3527}, {3295,9931}, {3564,5596}, {6243,12164}, {6759,8681}, {8193,9896}, {9820,11484}, {9926,11482}, {9927,11479}, {10659,11485}, {10660,11486}, {11411,11414}, {11432,12235}, {11441,12271}
X(12309) = reflection of X(i) in X(j) for these (i,j): (3,9937), (12301,9932)
X(12309) = orthologic center of these triangles: anti-incircle-circles to 2nd Hyacinth
X(12309) = X(84)-of-anti-incircle-circles-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(10112).
X(12310) lies on these lines: {3,125}, {4,12168}, {6,11800}, {22,3448}, {23,3564}, {25,110}, {26,9920}, {68,2937}, {74,11414}, {113,1598}, {155,5898}, {159,1177}, {161,542}, {373,12038}, {382,9932}, {399,7517}, {1511,6642}, {1593,10733}, {1597,12295}, {1995,7693}, {2079,6388}, {2771,9913}, {2930,6144}, {2948,8185}, {3527,5504}, {5020,5972}, {5594,7733}, {5595,7732}, {5609,12166}, {5654,7545}, {5663,7387}, {5889,12165}, {5899,12308}, {6800,8548}, {7514,11801}, {7687,11479}, {7984,8192}, {8276,8912}, {8277,10820}, {9517,11641}, {9714,12309}, {9818,10113}, {10037,10088}, {10046,10091}, {10620,11820}, {10663,11485}, {10664,11486}, {11365,11720}, {11426,12228}, {11432,12236}, {11441,12273}, {11456,12284}, {12082,12244}
X(12310) = reflection of X(i) in X(j) for these (i,j): (3,2931), (9919,7387), (12164,399)
X(12310) = X(104)-of-anti-incircle-circles-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(3).
X(12311) lies on these lines: {3,486}, {4,12169}, {487,1598}, {642,11484}, {1597,12296}, {3564,12312}, {11414,12221}, {11426,12229}, {11432,12237}, {11441,12274}, {11456,12285}
X(12311) = orthic-to-anti-incircle-circles similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12312) lies on these lines: {3,485}, {4,12170}, {488,1598}, {641,11484}, {1597,12297}, {3564,12311}, {11414,12222}, {11426,12230}, {11432,12238}, {11441,12275}, {11456,12286}
X(12312) = orthic-to-anti-incircle-circles similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12313) lies on these lines: {3,6}, {4,12171}, {5,487}, {25,6239}, {30,12257}, {51,5407}, {999,7362}, {1353,12256}, {1597,12298}, {1598,6291}, {1600,9777}, {3155,3167}, {3295,6283}, {3564,6462}, {5020,5409}, {6252,10306}, {8964,11427}, {9823,11484}, {9909,10132}, {11414,12223}, {11441,12276}, {11456,12287}, {11949,12311}
X(12313) = reflection of X(3) in X(1151)
X(12313) = {X(3),X(1351)}-harmonic conjugate of X(12314)
X(12313) = X(176)-of-anti-incircle-circles-triangle if ABC is acute
X(12313) = orthic-to-anti-incircle-circles similarity image of X(6291)
X(12313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,3311,5050), (3,5093,372), (6,9738,3)
The reciprocal orthologic center of these triangles is X(3).
X(12314) lies on these lines: {3,6}, {4,12172}, {5,488}, {25,6400}, {30,12256}, {51,5406}, {999,7353}, {1353,12257}, {1597,12299}, {1598,6406}, {1599,9777}, {3156,3167}, {3295,6405}, {3564,6463}, {5020,5408}, {6404,10306}, {9824,11484}, {9909,10133}, {11414,12224}, {11441,12277}, {11456,12288}, {11950,12312}
X(12314) = reflection of X(3) in X(1152)
X(12314) = {X(3),X(1351)}-harmonic conjugate of X(12313)
X(12314) = X(175)-of-anti-incircle-circles-triangle if ABC is acute
X(12314) = orthic-to-anti-incircle-circles similarity image of X(6406)
X(12314) = {X(6), X(9739)}-harmonic conjugate of X(3)
The reciprocal orthologic center of these triangles is X(389).
X(12315) lies on these lines: {3,64}, {4,3527}, {5,5544}, {20,11820}, {24,12112}, {25,6241}, {30,6193}, {54,1593}, {185,1598}, {221,6767}, {381,2883}, {382,1351}, {550,11206}, {999,7355}, {1181,1597}, {1482,6001}, {1614,3516}, {1656,6247}, {1657,9833}, {1853,3851}, {2192,7373}, {2777,12308}, {3146,12160}, {3167,12085}, {3295,6285}, {3517,10605}, {3579,9899}, {5054,6696}, {5073,5895}, {5198,5890}, {5663,7387}, {6254,10306}, {6449,10533}, {6450,10534}, {7592,11403}, {7973,8148}, {8549,9968}, {9707,11410}, {9729,11484}, {9909,12163}, {9914,9920}, {9934,10620}, {10076,10535}, {10675,11485}, {10676,11486}, {10721,12165}, {11414,12111}, {11441,12279}
X(12315) = reflection of X(i) in X(j) for these (i,j): (3,1498), (64,6759), (382,5878), (1657,9833), (5073,5895), (8148,7973), (8549,9968), (9899,3579), (10620,9934), (12250,550)
X(12315) = Stammler circle-inverse-of-X(6760)
X(12315) = X(8)-of-anti-incircle-circles-triangle if ABC is acute
X(12315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (154,3357,3), (1181,1597,11426), (1181,11381,1597), (1593,12290,3426), (7592,11455,11403), (8567,11202,3), (10282,10606,3), (11206,12250,550), (11456,12290,1593)
The reciprocal orthologic center of these triangles is X(6243).
X(12316) lies on these lines: {3,54}, {4,12175}, {24,2914}, {25,6242}, {64,10628}, {146,382}, {155,5898}, {381,2888}, {394,10115}, {399,10263}, {539,3830}, {999,7356}, {1209,5055}, {1351,3818}, {1482,5693}, {1597,12300}, {1598,6152}, {1656,11803}, {1657,12254}, {2937,7712}, {3295,6286}, {3519,3527}, {3526,8254}, {4550,11424}, {5070,5544}, {5073,5895}, {5899,6243}, {6255,10306}, {6515,10255}, {9703,10274}, {9827,11484}, {9977,11482}, {10677,11485}, {10678,11486}, {11414,12226}, {11426,12234}, {11432,12242}, {11441,12280}, {11456,12291}
X(12316) = reflection of X(i) in X(j) for these (i,j): (3,195), (1657,12254), (3519,3574), (7691,1493), (12307,54)
X(12316) = Stammler circle-inverse-of-X(1157)
X(12316) = X(79)-of-anti-incircle-circles-triangle if ABC is acute
X(12316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54,12307,3), (195,12307,54)
The reciprocal orthologic center of these triangles is X(3581).
X(12317) lies on these lines: {2,399}, {3,5900}, {4,94}, {5,12308}, {8,2771}, {20,10620}, {69,74}, {110,631}, {113,3545}, {125,3090}, {427,12165}, {497,7727}, {541,6515}, {1056,3028}, {1370,12219}, {1511,3524}, {1553,5627}, {1992,9976}, {2550,7724}, {2930,10519}, {2931,7556}, {2948,5657}, {3525,5609}, {3528,12041}, {3529,11411}, {3533,5972}, {3564,7464}, {3580,12112}, {3616,11699}, {3818,5890}, {3832,11801}, {4295,11670}, {4846,11442}, {5071,5655}, {5422,10821}, {5946,7693}, {5984,7422}, {6126,10056}, {6193,12302}, {6361,9904}, {6643,7723}, {6776,8546}, {7343,10072}, {7392,9826}, {7408,11566}, {7552,11456}, {7687,10706}, {10628,12284}, {10657,11488}, {10658,11489}, {11003,11597}, {11061,11579}, {11382,12140}, {11427,12227}, {11440,12254}, {11457,12281}, {12088,12310}
X(12317) = reflection of X(i) in X(j) for these (i,j): (4,3448), (20,10620), (146,265), (399,10264), (3529,12244), (6193,12302), (6361,9904), (11061,11579), (12112,3580), (12308,5)
X(12317) = anticomplement of X(399)
X(12317) = X(80)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12317) = antipode of X(4) in rectangular hyperbola passing through X(4), X(8), and the extraversions of X(8)
X(12317) = anticomplementary circle-inverse-of-X(265)
X(12317) = orthologic center of these triangles: anti-inverse-in-incircle to orthocentroidal
X(12317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (146,265,4), (146,3448,265), (399,10264,2)
The reciprocal orthologic center of these triangles is X(7387).
X(12318) lies on these lines: {2,9937}, {4,155}, {5,12309}, {20,12301}, {54,6815}, {68,69}, {376,9938}, {427,12166}, {497,9931}, {631,9932}, {1147,7401}, {1370,2013}, {1992,9926}, {3147,8907}, {3167,7528}, {6403,11382}, {6816,11487}, {7392,9820}, {10659,11488}, {10660,11489}, {11433,12235}, {11442,12271}
X(12318) = reflection of X(i) in X(j) for these (i,j): (20,12301), (12309,5)
X(12318) = anticomplement of X(9937)
X(12318) = X(84)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12318) = orthologic center of these triangles: anti-inverse-in-incircle to 2nd Hyacinth
The reciprocal orthologic center of these triangles is X(10112).
X(12319) lies on these lines: {2,2931}, {4,110}, {5,12310}, {20,12302}, {30,9919}, {69,265}, {74,1370}, {125,6643}, {146,7391}, {323,3153}, {427,12168}, {3448,11411}, {3564,7574}, {5972,7401}, {6699,7386}, {9927,11444}, {10272,11818}, {10663,11488}, {10664,11489}, {11427,12228}, {11433,12236}, {11442,12273}, {11457,12284}
X(12319) = reflection of X(i) in X(j) for these (i,j): (20,12302), (11411,3448), (12310,5)
X(12319) = anticomplement of X(2931)
X(12319) = X(104)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12319) = anticomplementary-circle-inverse-of-X(1300)
X(12319) = {X(110), X(10733)}-harmonic conjugate of X(12140)
The reciprocal orthologic center of these triangles is X(3).
X(12320) lies on these lines: {4,487}, {5,12311}, {20,12303}, {427,12169}, {486,7386}, {642,7392}, {1370,12221}, {3564,12321}, {10996,12123}, {11427,12229}, {11433,12237}, {11442,12274}, {11457,12285}
X(12320) = orthic-to-anti-inverse-in-incircle similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12321) lies on these lines: {4,488}, {5,12312}, {20,12304}, {427,12170}, {485,7386}, {641,7392}, {1370,12222}, {3564,12320}, {10996,12124}, {11427,12230}, {11433,12238}, {11442,12275}, {11457,12286}
X(12321) = orthic-to-anti-inverse-in-incircle similarity image of X(488)
The reciprocal orthologic center of these triangles is X(3).
X(12322) lies on these lines: {2,489}, {4,69}, {5,487}, {6,12221}, {20,492}, {30,488}, {183,7000}, {193,3070}, {325,7374}, {376,7690}, {388,7362}, {427,12171}, {486,11291}, {490,1270}, {491,3091}, {497,6283}, {524,12222}, {615,5023}, {639,6561}, {641,11147}, {1007,6811}, {1271,3832}, {1370,12223}, {1587,1992}, {1588,3618}, {2550,6252}, {3069,11293}, {3522,3593}, {3595,5068}, {3619,7388}, {5491,6251}, {5590,11294}, {6214,12296}, {6289,6337}, {6460,7823}, {7392,9823}, {8979,9306}, {10667,11488}, {10668,11489}, {11427,12231}, {11433,12239}, {11442,12276}, {11457,12287}
X(12322) = reflection of X(i) in X(j) for these (i,j): (20,12305), (12313,5)
X(12322) = anticomplement of X(1151)
X(12322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,69,12323), (4,637,69)
X(12322) = X(176)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12322) = orthic-to-anti-inverse-in-incircle similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12323) lies on these lines: {2,490}, {4,69}, {5,488}, {6,12222}, {20,491}, {30,487}, {183,7374}, {193,3071}, {325,7000}, {376,7692}, {388,7353}, {427,12172}, {485,11292}, {489,1271}, {492,3091}, {497,6405}, {524,12221}, {590,5023}, {640,6560}, {642,11147}, {1007,6813}, {1270,3832}, {1370,12224}, {1587,3618}, {1588,1992}, {2550,6404}, {3068,11294}, {3522,3595}, {3593,5068}, {3619,7389}, {5490,6250}, {5591,11293}, {6215,12297}, {6290,6337}, {6459,7823}, {7392,9824}, {10671,11488}, {10672,11489}, {11427,12232}, {11433,12240}, {11442,12277}, {11457,12288}
X(12323) = reflection of X(i) in X(j) for these (i,j): (20,12306), (12314,5)
X(12323) = anticomplement of X(1152)
X(12323) = X(175)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12323) = orthic-to-anti-inverse-in-incircle similarity image of X(6406)
X(12323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,69,12322), (4,638,69)
The reciprocal orthologic center of these triangles is X(389).
X(12324) lies on these lines: {2,1498}, {3,11206}, {4,51}, {5,5544}, {8,6001}, {20,64}, {30,11411}, {66,6815}, {125,6622}, {154,3523}, {376,3357}, {388,7355}, {427,12174}, {497,6285}, {511,2013}, {516,9899}, {631,5651}, {1158,6350}, {1181,3088}, {1352,10996}, {1370,12111}, {1559,6526}, {1593,6776}, {1853,2883}, {1895,10365}, {1992,8549}, {2550,6254}, {2777,12317}, {2917,7492}, {3146,6515}, {3332,7513}, {3522,10606}, {3524,10282}, {3527,11431}, {3538,11793}, {3541,11456}, {3543,5895}, {3575,11382}, {3839,5893}, {4293,10076}, {4294,10060}, {4295,7282}, {5059,5925}, {5596,7503}, {5663,12319}, {5731,12262}, {5907,7386}, {6193,12085}, {6643,12162}, {6995,9786}, {6997,10574}, {7288,10535}, {7378,12233}, {7392,9729}, {7408,11745}, {7487,10605}, {7505,12112}, {7544,7729}, {7667,11821}, {8567,10304}, {10192,10303}, {10299,11202}, {10675,11488}, {10676,11489}, {11245,11403}, {11442,12279}
X(12324) = reflection of X(i) in X(j) for these (i,j): (20,64), (1498,6247), (5059,5925), (6193,12085), (6225,4), (9833,3357), (12315,5)
X(12324) = anticomplement of X(1498)
X(12324) = anticomplementary-circle-inverse of X(34170)
X(12324) = X(8)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5,12315,5656), (154,6696,3523), (1181,3088,11427), (1498,6247,2), (1853,2883,3091), (1899,11381,4), (3357,9833,376), (11457,12290,4)
The reciprocal orthologic center of these triangles is X(6243).
X(12325) lies on these lines: {2,195}, {4,93}, {5,12316}, {8,6951}, {20,10620}, {24,11898}, {54,69}, {68,12319}, {155,7552}, {184,10203}, {323,6143}, {376,539}, {388,7356}, {427,12175}, {497,6286}, {1205,11457}, {1209,3090}, {1352,7730}, {1370,12226}, {1493,3525}, {1992,9977}, {2550,6255}, {2895,6853}, {2914,7505}, {2917,2930}, {2937,5898}, {3060,6153}, {3448,6101}, {3524,10610}, {3529,12324}, {3533,6689}, {3545,3574}, {3564,7512}, {5056,11803}, {5067,5645}, {5657,9905}, {5878,10628}, {5889,7706}, {7392,9827}, {9920,12088}, {10677,11488}, {10678,11489}, {11427,12234}, {11433,12242}, {11442,12280}
X(12325) = reflection of X(i) in X(j) for these (i,j): (4,2888), (20,12307), (2888,3519), (11271,54), (12254,7691), (12316,5)
X(12325) = anticomplement of X(195)
X(12325) = X(79)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(12325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3410,6243,4), (7691,12254,376)
The reciprocal orthologic center of these triangles is X(9855).
X(12326) lies on these lines: {30,12178}, {35,9875}, {55,671}, {56,9884}, {100,8591}, {115,4428}, {197,9876}, {542,11500}, {543,4421}, {1001,5461}, {1376,2482}, {2796,8715}, {3295,12258}, {5687,9881}, {8724,11499}, {9878,11494}, {9880,11496}, {9882,11497}, {9883,11498}, {10054,11507}, {10070,11508}, {10310,12117}, {11383,12132}, {11490,12191}, {11491,12243}
X(12326) = orthologic center of these triangles: anti-Mandart-incircle to McCay
X(12326) = X(671)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12327) lies on these lines: {3,11720}, {35,9904}, {40,2778}, {55,74}, {56,7978}, {100,146}, {110,10310}, {113,1376}, {125,11496}, {197,9919}, {541,4421}, {690,12178}, {1001,6699}, {2771,3811}, {2777,11500}, {2779,10620}, {2948,5537}, {3295,11709}, {5663,11248}, {7725,11497}, {7726,11498}, {7728,11499}, {9984,11494}, {10065,11507}, {10081,11508}, {10267,12041}, {11383,12133}, {11490,12192}, {11491,12244}
X(12327) = orthologic center of these triangles: anti-Mandart-incircle to orthocentroidal
X(12327) = X(74)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12328) lies on these lines: {3,914}, {35,9896}, {40,912}, {55,68}, {56,9933}, {100,6193}, {155,11499}, {197,9908}, {539,4421}, {1001,5449}, {1069,11502}, {1147,1376}, {3157,11501}, {3295,12259}, {5687,9928}, {9923,11494}, {9927,11496}, {9929,11497}, {9930,11498}, {10055,11507}, {10071,11508}, {10310,12118}, {11383,12134}, {11411,11491}, {11490,12193}
X(12328) = orthologic center of these triangles: anti-Mandart-incircle to 2nd Hyacinth
X(12328) = X(68)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12329) lies on these lines: {3,518}, {6,31}, {9,1486}, {10,7535}, {22,3681}, {25,210}, {35,3751}, {40,3827}, {41,4878}, {44,7083}, {48,2340}, {56,976}, {69,100}, {72,3556}, {141,1376}, {144,1633}, {159,197}, {165,7289}, {182,9052}, {198,480}, {206,219}, {220,1973}, {241,1037}, {354,7484}, {511,11248}, {517,9818}, {524,4421}, {573,2876}, {597,4428}, {611,4259}, {613,11508}, {1001,3589}, {1260,3185}, {1350,8679}, {1351,9047}, {1352,11499}, {1386,3295}, {1428,11510}, {1469,11509}, {1503,11500}, {1593,7957}, {1621,3618}, {1757,7295}, {1804,2283}, {1843,11383}, {1974,3690}, {2164,7077}, {2175,2911}, {2182,3059}, {2187,2318}, {2781,12327}, {2810,3098}, {3085,5800}, {3094,11494}, {3220,5223}, {3416,5687}, {3564,12328}, {3740,5020}, {3763,4413}, {3844,9709}, {3870,5314}, {3873,7485}, {3913,5846}, {3941,5120}, {3961,5329}, {4097,5847}, {4265,5217}, {4420,11337}, {4661,6636}, {5044,11365}, {5085,9049}, {5480,11496}, {5777,9911}, {5845,11495}, {5849,6776}, {6601,7397}, {8177,9055}, {9041,11194}, {9830,12326}, {10477,11517}, {11490,12212}
X(12329) = X(6)-of-anti-Mandart-incircle-triangle
X(12329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (72,8193,3556), (198,480,4557), (200,5285,197), (1631,4557,198), (2330,3779,6), (3242,5096,56), (5227,5285,159)
The reciprocal orthologic center of these triangles is X(40).
X(12330) lies on these lines: {3,960}, {35,7992}, {55,84}, {56,7971}, {109,1498}, {197,9910}, {268,3197}, {515,3913}, {516,8730}, {971,6600}, {999,5884}, {1001,6705}, {1012,3486}, {1035,2956}, {1260,1490}, {1376,6260}, {1657,2829}, {1709,11507}, {1768,7742}, {3149,3474}, {3295,5882}, {5658,10309}, {5880,6918}, {6244,11500}, {6245,11496}, {6257,11498}, {6258,11497}, {6259,11499}, {6796,11495}, {10085,11508}, {11383,12136}, {11490,12196}, {11491,12246}
X(12330) = X(84)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12331) lies on the Stammler circle and these lines: {1,6797}, {2,1484}, {3,8}, {4,11698}, {5,149}, {11,498}, {30,153}, {35,9897}, {40,2771}, {55,80}, {56,7972}, {119,381}, {145,6924}, {197,9912}, {214,1376}, {355,8715}, {382,5840}, {404,1483}, {517,3689}, {550,12248}, {971,2950}, {999,1317}, {1001,6702}, {1012,9963}, {1320,6911}, {1351,9024}, {1385,6264}, {1387,6767}, {1482,2802}, {1597,12138}, {1598,1862}, {1657,2829}, {1768,3579}, {2095,8730}, {2346,6881}, {2783,12188}, {2800,11500}, {2801,11495}, {2805,11258}, {3032,9567}, {3035,3526}, {3036,9708}, {3045,9704}, {3149,8148}, {3158,3577}, {3434,6980}, {3534,6244}, {3576,7993}, {3621,6942}, {3746,9956}, {3830,10711}, {4678,6875}, {5054,6174}, {5055,10707}, {5073,10728}, {5082,6863}, {5083,5708}, {5093,10755}, {5552,6971}, {5603,9802}, {5694,11010}, {5844,6905}, {5848,11898}, {5854,10680}, {6262,11498}, {6263,11497}, {6361,9809}, {6917,10528}, {6918,11729}, {6928,7080}, {6946,10283}, {9913,12083}, {10057,11507}, {10073,11508}, {10310,12119}, {11383,12137}, {11490,12198}
X(12331) = midpoint of X(i) and X(j) for these {i,j}: {40,5531}, {5541,6326}, {6361,9809}
X(12331) = reflection of X(i) in X(j) for these (i,j): (3,100), (4,11698), (149,5), (382,10742), (1482,6265), (1768,3579), (3830,10711), (5073,10728), (6264,1385), (8148,10698), (10738,119), (12247,5690), (12248,550)
X(12331) = X(80)-of-anti-Mandart-incircle-triangle
X(12331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11,10087,3295), (55,5790,7489), (100,6224,2932), (119,10738,381), (355,8715,11849), (1317,10090,999), (3913,11499,1482), (5690,11491,3)
X(12331) = anticomplement of X(1484)
The reciprocal orthologic center of these triangles is X(40).
X(12332) lies on these lines: {3,214}, {11,6833}, {20,100}, {55,104}, {56,10698}, {80,1012}, {84,5531}, {119,1376}, {197,9913}, {515,12331}, {528,8730}, {952,3913}, {1001,6713}, {1158,2771}, {1537,10090}, {2077,2932}, {2787,12178}, {2801,6600}, {2802,10306}, {3035,6825}, {3295,11715}, {3428,4996}, {5450,11849}, {5537,5541}, {5722,10265}, {6224,6909}, {6256,11698}, {6259,6796}, {6702,6913}, {6906,10950}, {8069,11570}, {10058,11507}, {10074,11508}, {10742,11499}, {11383,12138}, {11490,12199}, {11491,12248}
X(12332) = midpoint of X(i) and X(j) for these {i,j}: {84,5531}, {2950,6326}
X(12332) = reflection of X(i) in X(j) for these (i,j): (6256,11698), (11500,100)
X(12332) = X(104)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12333) lies on these lines: {35,9898}, {55,84}, {56,8000}, {100,9874}, {946,3295}, {1750,3746}, {3035,3526}, {3913,6684}, {6600,10267}, {8715,8730}, {10059,11507}, {10075,11508}, {10306,11495}, {10310,12120}, {11383,12139}, {11490,12200}, {11491,12249}
X(12333) = X(7160)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12334) lies on these lines: {30,12327}, {40,2771}, {55,265}, {110,11499}, {125,10267}, {542,12329}, {1376,1511}, {3295,12261}, {3448,11491}, {5663,11500}, {6911,11720}, {10088,11501}, {10091,11502}, {10113,11496}, {10310,12121}, {11383,12140}, {11490,12201}
X(12334) = X(265)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12335) lies on these lines: {30,12328}, {35,9899}, {40,197}, {55,64}, {56,7973}, {100,6225}, {199,5584}, {204,11471}, {1001,6696}, {1376,2883}, {1466,2192}, {1498,3682}, {1802,3197}, {2777,12334}, {3295,12262}, {3357,10267}, {3811,6001}, {3827,6769}, {5878,11499}, {6000,11248}, {6247,11496}, {6266,11498}, {6267,11497}, {6285,11509}, {8273,8567}, {10060,11507}, {10076,11508}, {11381,11383}, {11490,12202}, {11491,12250}
X(12335) = X(64)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12336) lies on these lines: {14,55}, {35,9900}, {56,7974}, {100,617}, {197,9915}, {530,12326}, {531,4421}, {542,12329}, {619,1376}, {1001,6670}, {3295,11706}, {4428,5460}, {5474,10310}, {5479,11496}, {5613,11499}, {6269,11498}, {6271,11497}, {6773,11491}, {6774,10267}, {9981,11494}, {10061,11507}, {10077,11508}, {11383,12141}, {11490,12204}
X(12336) = X(14)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12337) lies on these lines: {13,55}, {35,9901}, {56,7975}, {100,616}, {197,9916}, {530,4421}, {531,12326}, {542,12329}, {618,1376}, {1001,6669}, {3295,11705}, {4428,5459}, {5473,10310}, {5478,11496}, {5617,11499}, {6268,11498}, {6270,11497}, {6770,11491}, {6771,10267}, {9982,11494}, {10062,11507}, {10078,11508}, {11383,12142}, {11490,12205}
X(12337) = X(13)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12338) lies on these lines: {3,730}, {35,9902}, {39,1376}, {55,76}, {56,7976}, {100,194}, {197,9917}, {384,11490}, {511,11500}, {538,4421}, {726,8715}, {732,12329}, {1001,3934}, {2782,11248}, {3095,11499}, {3295,12263}, {4413,7786}, {4428,9466}, {5969,12326}, {6248,11496}, {6272,11498}, {6273,11497}, {9983,11494}, {10063,11507}, {10079,11508}, {10310,11257}, {11383,12143}, {11491,12251}
X(12338) = X(76)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12339) lies on these lines: {35,9903}, {55,83}, {56,7977}, {100,2896}, {197,9918}, {732,12329}, {754,4421}, {1001,6704}, {1376,6292}, {3295,12264}, {6249,11496}, {6274,11498}, {6275,11497}, {6287,11499}, {10064,11507}, {10080,11508}, {10310,12122}, {11383,12144}, {11490,12206}, {11491,12252}
X(12339) = X(83)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12340) lies on these lines: {3,11722}, {55,1297}, {112,10310}, {127,11496}, {132,1376}, {2799,12178}, {2806,12332}, {3295,12265}, {4421,9530}, {6020,11509}, {9517,12327}, {11383,12145}, {11490,12207}, {11491,12253}
X(12340) = X(1297)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12341) lies on these lines: {35,9905}, {54,55}, {56,7979}, {100,2888}, {195,11849}, {197,9920}, {539,4421}, {692,10274}, {1001,6689}, {1154,11248}, {1209,1376}, {3295,12266}, {3574,11496}, {6276,11498}, {6277,11497}, {6288,11499}, {7691,10310}, {9985,11494}, {10066,11507}, {10082,11508}, {10267,10610}, {10628,12327}, {11383,11576}, {11490,12208}, {11491,12254}
X(12341) = X(54)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12342) lies on these lines: {55,10266}, {149,2975}, {3295,12267}, {3913,5904}, {11383,12146}, {11490,12209}, {11491,12255}
X(12342) = X(10266)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12343) lies on these lines: {35,9906}, {55,486}, {56,7980}, {100,487}, {197,9921}, {642,1376}, {1001,6119}, {3295,12268}, {3564,12328}, {6251,11496}, {6280,11498}, {6281,11497}, {6290,11499}, {9986,11494}, {10067,11507}, {10083,11508}, {10310,12123}, {11383,12147}, {11490,12210}, {11491,12256}
X(12343) = X(486)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12344) lies on these lines: {35,9907}, {55,485}, {56,7981}, {100,488}, {197,9922}, {641,1376}, {1001,6118}, {3295,12269}, {3564,12328}, {6250,11496}, {6278,11498}, {6279,11497}, {6289,11499}, {9987,11494}, {10068,11507}, {10084,11508}, {10310,12124}, {11383,12148}, {11490,12211}, {11491,12257}
X(12344) = X(485)-of-anti-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12345) lies on these lines: {30,12179}, {543,11207}, {671,5597}, {2482,5599}, {5598,9884}, {5601,8591}, {8190,9876}, {8196,9880}, {8197,9881}, {8198,9882}, {8199,9883}, {8200,8724}, {9878,11861}, {10054,11877}, {10070,11879}, {11366,12258}, {11384,12132}, {11492,12326}, {11822,12117}, {11837,12191}, {11843,12243}
X(12345) = X(671)-of-1st-Auriga-triangle
X(12345) = X(9884)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12346) lies on these lines: {30,12180}, {55,12345}, {543,11208}, {671,5598}, {2482,5600}, {5597,9884}, {5602,8591}, {8187,9875}, {8191,9876}, {8203,9880}, {8204,9881}, {8205,9882}, {8206,9883}, {8207,8724}, {9878,11862}, {10054,11878}, {10070,11880}, {11367,12258}, {11385,12132}, {11493,12326}, {11823,12117}, {11838,12191}, {11844,12243}
X(12346) = X(671)-of-2nd-Auriga-triangle
X(12346) = X(9884)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12347) lies on these lines: {30,99}, {402,671}, {542,12113}, {543,1651}, {1650,2482}, {4240,8591}, {9875,11852}, {9876,11853}, {9878,11885}, {9880,11897}, {9881,11900}, {9882,11901}, {9883,11902}, {9884,11910}, {10054,11912}, {10070,11913}, {11831,12258}, {11832,12132}, {11839,12191}, {11845,12243}, {11848,12326}, {11863,12345}, {11864,12346}
X(12347) = midpoint of X(4240) and X(8591)
X(12347) = reflection of X(i) in X(j) for these (i,j): (671,402), (1650,2482)
X(12347) = X(671)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12348) lies on these lines: {11,671}, {30,12182}, {355,8724}, {542,12114}, {543,11235}, {1376,2482}, {3434,8591}, {9875,10826}, {9876,10829}, {9878,10871}, {9880,10893}, {9881,10914}, {9882,10919}, {9883,10920}, {9884,10944}, {10054,10523}, {10070,10948}, {10785,12243}, {10794,12191}, {11373,12258}, {11390,12132}, {11826,12117}, {11865,12345}, {11866,12346}, {11903,12347}
X(12348) = reflection of X(12326) in X(2482)
X(12348) = reflection of X(12349) in X(8724)
X(12348) = X(671)-of-inner-Johnson-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12349) lies on these lines: {12,671}, {30,12183}, {72,9881}, {355,8724}, {542,11500}, {543,11236}, {958,2482}, {3436,8591}, {9875,10827}, {9876,10830}, {9878,10872}, {9880,10894}, {9882,10921}, {9883,10922}, {9884,10950}, {10054,10954}, {10070,10523}, {10786,12243}, {10795,12191}, {11374,12258}, {11391,12132}, {11827,12117}, {11867,12345}, {11868,12346}, {11904,12347}
X(12349) = reflection of X(12348) in X(8724)
X(12349) = X(671)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12350) lies on these lines: {1,8724}, {2,3027}, {5,10070}, {12,671}, {55,542}, {56,2482}, {65,9881}, {98,4995}, {99,5434}, {114,11238}, {147,10385}, {226,2796}, {388,8591}, {495,10054}, {543,11237}, {2276,6034}, {2782,10056}, {3028,11006}, {3058,6054}, {3085,12243}, {3584,11632}, {5261,8596}, {7354,12117}, {9578,9875}, {9657,10992}, {9876,10831}, {9878,10873}, {9880,10895}, {9882,10923}, {9883,10924}, {9884,10944}, {10797,12191}, {11375,12258}, {11392,12132}, {11501,12326}, {11869,12345}, {11870,12346}, {11905,12347}
X(12350) = reflection of X(10054) in X(495)
X(12350) = X(671)-of-1st-Johnson-Yff-triangle
X(12350) = {X(1), X(8724)}-harmonic conjugate of X(12351)
X(12350) = {X(3058), X(6054)}-harmonic conjugate of X(12185)
The reciprocal orthologic center of these triangles is X(9855).
X(12351) lies on these lines: {1,8724}, {2,3023}, {5,10054}, {11,671}, {30,10089}, {55,2482}, {56,542}, {98,5298}, {99,3058}, {114,11237}, {496,10070}, {497,8591}, {543,11238}, {549,10053}, {2275,6034}, {2782,10072}, {2796,12053}, {3057,9881}, {3086,12243}, {3582,11632}, {5182,10799}, {5274,8596}, {5434,6054}, {6284,12117}, {9581,9875}, {9670,10992}, {9876,10832}, {9878,10874}, {9880,10896}, {9882,10925}, {9883,10926}, {9884,10950}, {10798,12191}, {11376,12258}, {11393,12132}, {11502,12326}, {11871,12345}, {11872,12346}, {11906,12347}
X(12351) = reflection of X(10070) in X(496)
X(12351) = X(671)-of-2nd-Johnson-Yff-triangle
X(12351) = {X(1), X(8724)}-harmonic conjugate of X(12350)
The reciprocal orthologic center of these triangles is X(9855).
X(12352) lies on these lines: {30,12186}, {493,671}, {542,9838}, {543,12152}, {2482,8222}, {6461,12353}, {6462,8591}, {8188,9875}, {8194,9876}, {8201,12345}, {8208,12346}, {8210,9884}, {8212,9880}, {8214,9881}, {8216,9882}, {8218,9883}, {8220,8724}, {9878,10875}, {10054,11951}, {10070,11953}, {10945,12348}, {10951,12349}, {11377,12258}, {11394,12132}, {11503,12326}, {11828,12117}, {11840,12191}, {11846,12243}, {11907,12347}, {11930,12350}, {11932,12351}
X(12352) = X(671)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12353) lies on these lines: {30,12187}, {494,671}, {542,9839}, {543,12153}, {2482,8223}, {6461,12352}, {6463,8591}, {8189,9875}, {8195,9876}, {8202,12345}, {8209,12346}, {8211,9884}, {8213,9880}, {8215,9881}, {8217,9882}, {8219,9883}, {8221,8724}, {9878,10876}, {10054,11952}, {10070,11954}, {10946,12348}, {10952,12349}, {11378,12258}, {11395,12132}, {11504,12326}, {11829,12117}, {11841,12191}, {11847,12243}, {11908,12347}, {11931,12350}, {11933,12351}
X(12353) = X(671)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12354) lies on these lines: {3,10070}, {4,12350}, {11,2482}, {12,9880}, {33,12132}, {55,671}, {56,12117}, {99,11238}, {115,4995}, {148,10385}, {390,8596}, {497,8591}, {542,6284}, {543,3023}, {950,2796}, {1479,8724}, {1697,9875}, {1837,9881}, {2098,9884}, {2646,12258}, {3056,9830}, {3295,10054}, {4294,12243}, {5182,10798}, {5432,5461}, {6034,9598}, {6321,10056}, {9876,10833}, {9878,10877}, {9882,10927}, {9883,10928}, {10799,12191}, {10947,12348}, {10953,12349}, {11873,12345}, {11874,12346}, {11909,12347}, {11947,12352}, {11948,12353}
X(12354) = reflection of X(3023) in X(3058)
X(12354) = X(671)-of-Mandart-incircle-triangle
X(12354) = {X(497), X(8591)}-harmonic conjugate of X(12351)
The reciprocal orthologic center of these triangles is X(9855).
X(12355) lies on these lines: {3,671}, {4,8596}, {5,8591}, {30,148}, {99,5055}, {114,381}, {115,5054}, {355,2796}, {382,542}, {517,9875}, {576,10488}, {999,10070}, {1351,9830}, {1598,12132}, {1656,2482}, {2782,3830}, {2936,7545}, {3295,10054}, {3526,5461}, {3534,11632}, {3655,11599}, {5093,8593}, {5790,9881}, {7517,9876}, {8787,11482}, {9654,12350}, {9669,12351}, {9882,11916}, {9883,11917}, {9884,10247}, {10246,12258}, {11152,11317}, {11656,12121}, {11842,12191}, {11849,12326}, {11875,12345}, {11876,12346}, {11911,12347}, {11928,12348}, {11929,12349}, {11949,12352}, {11950,12353}
X(12355) = midpoint of X(4) and X(8596)
X(12355) = reflection of X(i) in X(j) for these (i,j): (3,671), (381,6321), (3534,11632), (3655,11599), (8591,5), (8724,9880), (10488,576), (10992,5461), (12121,11656)
X(12355) = X(671)-of-X3-ABC-reflections-triangle
X(12355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6321,8724,9880), (8724,9880,381), (10054,12354,3295)
The reciprocal orthologic center of these triangles is X(9855).
X(12356) lies on these lines: {1,671}, {12,12348}, {30,12189}, {542,12115}, {543,11239}, {2482,5552}, {8591,10528}, {8724,10942}, {9876,10834}, {9878,10878}, {9880,10531}, {9881,10915}, {9882,10929}, {9883,10930}, {10803,12191}, {10805,12243}, {10955,12349}, {10956,12350}, {10958,12351}, {10965,12354}, {11248,12117}, {11400,12132}, {11509,12326}, {11881,12345}, {11882,12346}, {11914,12347}, {11955,12352}, {11956,12353}, {12000,12355}
X(12356) = reflection of X(671) in X(10054)
X(12356) = X(671)-of-inner-Yff-tangents-triangle
The reciprocal orthologic center of these triangles is X(9855).
X(12357) lies on these lines: {1,671}, {11,12349}, {30,12190}, {542,12116}, {543,11240}, {2482,10527}, {8591,10529}, {8724,10943}, {9876,10835}, {9878,10879}, {9880,10532}, {9881,10916}, {9882,10931}, {9883,10932}, {10804,12191}, {10806,12243}, {10949,12348}, {10957,12350}, {10959,12351}, {10966,12354}, {11249,12117}, {11401,12132}, {11510,12326}, {11883,12345}, {11884,12346}, {11915,12347}, {11957,12352}, {11958,12353}, {12001,12355}
X(12357) = reflection of X(671) in X(10070)
X(12357) = X(671)-of-outer-Yff-tangents-triangle
The reciprocal orthologic center of these triangles is X(3581).
X(12358) lies on these lines: {2,1986}, {3,74}, {5,1112}, {20,12292}, {30,12133}, {52,11746}, {69,265}, {113,127}, {125,5562}, {143,10255}, {182,12227}, {389,6723}, {394,5504}, {511,7687}, {526,6334}, {542,11574}, {631,7722}, {974,6699}, {1040,7727}, {1060,3028}, {1154,2072}, {1368,10264}, {2777,5907}, {2854,9967}, {2914,7550}, {2979,10733}, {3448,6643}, {3564,10111}, {5076,11387}, {5894,12162}, {5972,7542}, {6101,10113}, {6102,6640}, {6676,10272}, {6746,10224}, {7386,12317}, {7484,12165}, {7514,12228}, {7724,10319}, {7728,11487}, {9140,12273}, {9976,11511}, {10170,11557}, {10625,12295}, {10657,11515}, {10658,11516}, {11821,12121}
X(12358) = midpoint of X(i) and X(j) for these {i,j}: {3,7723}, {20,12292}, {125,5562}, {1986,12219}, {5876,12041}, {6101,10113}, {10625,12295}
X(12358) = reflection of X(i) in X(j) for these (i,j): (52,11746), (389,6723), (974,6699), (1112,5), (1986,9826), (5972,11793)
X(12358) = anticomplement of X(9826)
X(12358) = complement of X(1986)
X(12358) = orthologic center of these triangles: 6th anti-mixtilinear to orthocentroidal
X(12358) = X(80)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12358) = {X(2), X(12219)}-harmonic conjugate of X(1986)
The reciprocal orthologic center of these triangles is X(7387).
Let A'B'C' be as described at X(11585). Then X(12359) = X(4)-of-A'B'C'. (Randy Hutson, July 21, 2017)
X(12359) lies on these lines: {2,155}, {3,68}, {4,3580}, {5,389}, {10,912}, {11,6238}, {12,7352}, {20,12293}, {22,11457}, {24,11442}, {26,1503}, {30,3357}, {51,7403}, {52,427}, {55,10071}, {56,10055}, {69,3546}, {110,10018}, {125,5562}, {135,432}, {140,141}, {143,5480}, {156,10020}, {184,7542}, {235,12162}, {394,3548}, {403,12111}, {468,10539}, {498,3157}, {499,1069}, {511,12235}, {517,12259}, {524,8548}, {525,10279}, {539,549}, {542,10282}, {550,10264}, {568,5576}, {569,11245}, {590,10665}, {615,10666}, {631,6193}, {858,11412}, {1040,9931}, {1092,10257}, {1181,3549}, {1209,7399}, {1216,1368}, {1352,6642}, {1594,5889}, {1595,5446}, {1656,5544}, {2013,7999}, {2080,12193}, {2883,5663}, {2918,2931}, {3167,3526}, {3519,5504}, {3541,6515}, {3567,5133}, {3576,9896}, {3925,6237}, {5094,12160}, {5392,8800}, {5418,8909}, {5447,11574}, {6640,11064}, {6643,11821}, {6696,12084}, {7386,12318}, {7404,11433}, {7484,12166}, {7505,11441}, {7526,12241}, {7553,11550}, {7691,9140}, {7998,12271}, {8546,9925}, {9926,11511}, {9933,10246}, {10112,11430}, {10267,12328}, {10295,12278}, {10659,11515}, {10660,11516}, {11745,11818}
X(12359) = midpoint of X(i) and X(j) for these {i,j}: {3,68}, {4,12163}, {20,12293}, {155,11411}, {2931,3448}, {7689,9927}
X(12359) = reflection of X(i) in X(j) for these (i,j): (5,5449), (155,9820), (156,10020), (1147,140), (12084,6696)
X(12359) = anticomplement of X(9820)
X(12359) = complement of X(155)
X(12359) = X(68)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12359) = orthologic center of these triangles: 6th anti-mixtilinear to 2nd Hyacinth
X(12359) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,155,9820), (2,11411,155), (5,6102,12233), (24,11442,12134), (125,5562,11585), (156,10020,10192), (1209,9730,7399), (1656,12164,5654)
The reciprocal orthologic center of these triangles is X(3).
X(12360) lies on these lines: {2,6291}, {3,6}, {20,12298}, {488,8681}, {631,6239}, {1038,7362}, {1040,6283}, {6252,10319}, {7386,12322}, {7484,12171}, {7998,12276}, {7999,12287}, {8909,12230}, {9822,11292}
X(12360) = midpoint of X(i) and X(j) for these {i,j}: {20,12298}, {6291,12223}
X(12360) = reflection of X(6291) in X(9823)
X(12360) = anticomplement of X(9823)
X(12360) = complement of X(6291)
X(12360) = {X(3),X(11574)}-harmonic conjugate of X(12361)
X(12360) = X(176)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12360) = orthic-to-6th-anti-mixtilinear similarity image of X(6291)
The reciprocal orthologic center of these triangles is X(3).
X(12361) lies on these lines: {2,6406}, {3,6}, {20,12299}, {487,8681}, {631,6400}, {1038,7353}, {1040,6405}, {5943,8964}, {6404,10319}, {7386,12323}, {7484,12172}, {7998,12277}, {7999,12288}, {9822,11291}
X(12361) = midpoint of X(i) and X(j) for these {i,j}: {20,12299}, {6406,12224}
X(12361) = reflection of X(6406) in X(9824)
X(12361) = anticomplement of X(9824)
X(12361) = complement of X(6406)
X(12361) = {X(3),X(11574)}-harmonic conjugate of X(12360)
X(12361) = X(175)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12361) = orthic-to-6th-anti-mixtilinear similarity image of X(6406)
The reciprocal orthologic center of these triangles is X(4).
As a point on the Euler line, X(12362) has Shinagawa coefficients: (E+F, -E-3*F).
X(12362) lies on these lines: {2,3}, {69,11821}, {182,12233}, {206,2883}, {216,7745}, {511,12241}, {524,10112}, {577,5254}, {1038,7354}, {1040,6284}, {1060,4320}, {1062,4319}, {1352,9924}, {1353,12160}, {1503,5907}, {1578,6560}, {1579,6561}, {2968,5015}, {3070,11513}, {3071,11514}, {3292,10619}, {3564,4173}, {3580,7691}, {4549,12163}, {4911,6356}, {5305,10316}, {5318,11515}, {5321,11516}, {5889,11245}, {5891,11750}, {5943,11745}, {5965,12024}, {6253,10319}, {6389,7784}, {6776,12164}, {7583,10897}, {7584,10898}, {7998,12278}, {7999,12289}, {8550,11511}, {10634,11542}, {10635,11543}, {11412,12022}
X(12362) = midpoint of X(i) and X(j) for these {i,j}: {20,1885}, {3575,12225}, {5562,6146}, {11750,12134}
X(12362) = reflection of X(i) in X(j) for these (i,j): (3575,9825), (6756,5), (7576,10128)
X(12362) = anticomplement of X(9825)
X(12362) = complement of X(3575)
X(12362) = X(65)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12362) = X(4)-of-3rd-pedal-triangle-of-X(3)
X(12362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,12225,3575), (3,4,6823), (3,5,6676), (3,381,3547), (3,2072,7542), (4,7395,5), (4,7509,7399), (5,550,26), (5,3627,11818), (5,7715,7529), (5,10154,3542), (20,6816,25), (25,6816,5), (376,3542,9715), (1885,7667,20), (2043,2044,9909), (2072,7542,3628), (3091,7539,5), (3542,9715,10154), (6804,7487,5020), (10024,10297,3850)
The reciprocal orthologic center of these triangles is X(6243).
X(12363) lies on these lines: {2,6152}, {3,54}, {5,11576}, {20,12300}, {69,3519}, {140,6746}, {141,1209}, {182,12234}, {511,12242}, {539,1216}, {631,6242}, {973,5462}, {1038,7356}, {1040,6286}, {1656,6403}, {2888,6643}, {3917,12359}, {5447,6699}, {5562,10619}, {5894,10575}, {5907,12134}, {5965,11574}, {6193,11821}, {6243,11427}, {6255,10319}, {6288,11487}, {6676,8254}, {7386,12325}, {7484,12175}, {7730,11465}, {7998,12280}, {7999,12291}, {9977,11511}, {10625,12233}, {10677,11515}, {10678,11516}, {12358,12362}
X(12363) = midpoint of X(i) and X(j) for these {i,j}: {20,12300}, {1493,6101}, {5562,10619}, {6152,12226}
X(12363) = reflection of X(i) in X(j) for these (i,j): (973,6689), (6152,9827), (11576,5)
X(12363) = anticomplement of X(9827)
X(12363) = complement of X(6152)
X(12363) = X(79)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(12363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,12226,6152), (54,1993,1493)
The reciprocal orthologic center of these triangles is X(9934).
X(12364) lies on these lines: {5,6}, {74,323}, {113,539}, {186,12273}, {399,1514}, {974,10816}, {1147,10574}, {9938,12164}, {11456,12118}
X(12364) = orthologic center of these triangles: anti-orthocentroidal to 2nd Hyacinth
X(12364) = X(5504)-of-anti-orthocentroidal-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12365) lies on these lines: {55,12366}, {74,5597}, {110,11822}, {113,5599}, {125,8196}, {146,5601}, {541,11207}, {690,12179}, {3028,11873}, {5598,7978}, {5663,11252}, {7725,8198}, {7726,8199}, {7728,8200}, {10065,11877}, {10081,11879}, {10620,11875}, {11366,11709}, {11492,12327}, {11837,12192}, {11843,12244}
X(12365) = reflection of X(12366) in X(55)
X(12365) = X(74)-of-1st-Auriga-triangle
X(12365) = X(7978)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12366) lies on these lines: {55,12365}, {74,5598}, {110,11823}, {113,5600}, {125,8203}, {146,5602}, {541,11208}, {690,12180}, {3028,11874}, {5597,7978}, {5663,11253}, {7725,8205}, {7726,8206}, {7728,8207}, {8187,9904}, {10065,11878}, {10081,11880}, {10620,11876}, {11367,11709}, {11493,12327}, {11838,12192}, {11844,12244}
X(12366) = reflection of X(12365) in X(55)
X(12366) = X(74)-of-2nd-Auriga-triangle
X(12366) = X(7978)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(9970).
X(12367) lies on these lines: {6,25}, {23,2854}, {30,5648}, {50,5191}, {67,74}, {110,8705}, {156,11663}, {187,5938}, {237,9142}, {323,9019}, {399,511}, {512,5104}, {542,3581}, {597,10545}, {599,3098}, {1614,12061}, {1995,8547}, {2781,12112}, {3448,8262}, {5640,8546}, {7575,11579}, {10540,11649}
X(12367) = reflection of X(i) in X(j) for these (i,j): (6,1495), (3448,8262), (10510,110), (11579,7575)
X(12367) = X(67)-of-anti-orthocentroidal-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12368) lies on these lines: {1,113}, {2,11709}, {8,146}, {10,74}, {40,2777}, {65,79}, {72,2778}, {110,515}, {125,5587}, {355,5663}, {381,12261}, {516,10721}, {517,7728}, {519,7978}, {541,3679}, {542,3751}, {690,9864}, {944,11720}, {946,7984}, {1698,6699}, {1737,10081}, {1837,3028}, {2779,5086}, {2781,3416}, {2931,8185}, {2948,5691}, {3465,4551}, {3576,5972}, {3822,5494}, {5090,12133}, {5655,11699}, {5657,12244}, {5687,12327}, {5688,7726}, {5689,7725}, {5777,10693}, {5790,10620}, {5847,10752}, {8193,9919}, {8197,12365}, {8204,12366}, {8227,11735}, {8998,9583}, {9798,12168}, {9857,9984}, {10039,10065}, {10088,10572}, {10791,12192}
X(12368) = midpoint of X(i) and X(j) for these {i,j}: {8,146}, {2948,5691}
X(12368) = reflection of X(i) in X(j) for these (i,j): (1,113), (74,10), (944,11720), (7984,946), (10693,5777)
X(12368) = anticomplement of X(11709)
X(12368) = X(74)-of-outer-Garcia-triangle
X(12368) = X(1)-of-X(30)-Fuhrmann-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12369) lies on these lines: {30,110}, {74,402}, {113,1650}, {125,11897}, {146,4240}, {541,1651}, {690,12181}, {2777,7740}, {3028,11909}, {5663,11251}, {7725,11901}, {7726,11902}, {7978,11910}, {9904,11852}, {9919,11853}, {9984,11885}, {10065,11912}, {10081,11913}, {10620,11911}, {11709,11831}, {11832,12133}, {11839,12192}, {11845,12244}, {11848,12327}, {11900,12368}
X(12369) = midpoint of X(146) and X(4240)
X(12369) = reflection of X(i) in X(j) for these (i,j): (74,402), (1650,113)
X(12369) = X(74)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(399).
X(12370) lies on these lines: {3,3580}, {4,1994}, {5,578}, {6,12293}, {23,12254}, {30,52}, {49,403}, {54,10024}, {68,7526}, {113,137}, {143,3575}, {156,235}, {265,1594}, {382,12174}, {389,11800}, {539,5907}, {568,6240}, {576,1353}, {1352,9925}, {1614,11799}, {1885,5663}, {1899,12084}, {2777,11232}, {3060,12289}, {3564,5876}, {3567,12278}, {5133,6288}, {5446,10115}, {5449,11430}, {6000,10116}, {6101,12362}, {6243,12225}, {6644,12118}, {6676,10610}, {6696,10264}, {7530,9833}, {9818,12166}, {10274,11563}, {10982,11818}, {11536,12227}
X(12370) = midpoint of X(6243) and X(12225)
X(12370) = reflection of X(i) in X(j) for these (i,j): (5,12241), (3575,143), (6101,12362), (11819,5446), (12134,546)
X(12370) = X(1)-of-1st-Hyacinth-triangle if ABC is acute
X(12370) = {X(578), X(9927)}-harmonic conjugate of X(5)
The reciprocal orthologic center of these triangles is X(12112).
X(12371) lies on these lines: {11,74}, {110,11826}, {113,1376}, {125,10893}, {146,3434}, {355,7728}, {541,11235}, {690,12182}, {2777,12114}, {3028,10947}, {5663,10525}, {7725,10919}, {7726,10920}, {7978,10944}, {9904,10826}, {9919,10829}, {9984,10871}, {10065,10523}, {10081,10948}, {10620,11928}, {10785,12244}, {10794,12192}, {10914,12368}, {11373,11709}, {11390,12133}, {11865,12365}, {11866,12366}, {11903,12369}
X(12371) = reflection of X(12327) in X(113)
X(12371) = reflection of X(12372) in X(7728)
X(12371) = X(74)-of-inner-Johnson-triangle
X(12371) = X(12381)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12372) lies on these lines: {12,74}, {72,2778}, {110,11827}, {113,958}, {125,10894}, {146,3436}, {265,2779}, {355,7728}, {541,11236}, {690,12183}, {2777,11500}, {3028,10953}, {5663,10526}, {6253,10721}, {7725,10921}, {7726,10922}, {7978,10950}, {9904,10827}, {9919,10830}, {9984,10872}, {10065,10954}, {10081,10523}, {10620,11929}, {10786,12244}, {10795,12192}, {11374,11709}, {11391,12133}, {11867,12365}, {11868,12366}, {11904,12369}
X(12372) = reflection of X(12371) in X(7728)
X(12372) = X(74)-of-outer-Johnson-triangle
X(12372) = X(12382)-of-inner-Johnson-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12373) lies on the inner-Johnson-Yff-circle and these lines: {1,7728}, {4,3028}, {5,10081}, {12,74}, {30,10088}, {55,2777}, {56,113}, {65,79}, {73,9627}, {110,7354}, {125,10895}, {146,388}, {495,10065}, {498,12041}, {541,11237}, {690,12184}, {1388,11723}, {1478,5663}, {1479,1539}, {1511,4299}, {2931,9658}, {2948,9579}, {3031,9553}, {3043,9652}, {3047,9653}, {3085,12244}, {3448,5229}, {5204,5972}, {5270,7727}, {5434,10706}, {6284,10721}, {7725,10923}, {7726,10924}, {7978,10944}, {9578,9904}, {9647,10819}, {9648,10817}, {9654,10620}, {9659,10117}, {9919,10831}, {9984,10873}, {10082,11805}, {10483,12121}, {10797,12192}, {11375,11709}, {11392,12133}, {11501,12327}, {11905,12369}
X(12373) = reflection of X(10065) in X(495)
X(12373) = X(74)-of-1st-Johnson-Yff-triangle
X(12373) = {X(1),X(7728)}-harmonic conjugate of X(12374)
The reciprocal orthologic center of these triangles is X(12112).
X(12374) lies on the outer-Johnson-Yff-circle and these lines: {1,7728}, {5,10065}, {11,74}, {30,10091}, {55,113}, {56,2777}, {110,6284}, {125,10896}, {146,497}, {265,3583}, {399,9668}, {496,10081}, {499,12041}, {541,11238}, {690,12185}, {1478,1539}, {1479,5663}, {1511,4302}, {2931,9673}, {2948,9580}, {3031,9554}, {3043,9667}, {3047,9666}, {3057,12368}, {3058,10706}, {3086,12244}, {3448,5225}, {5217,5972}, {7354,10721}, {7725,10925}, {7726,10926}, {7978,10950}, {9581,9904}, {9630,10118}, {9660,10819}, {9663,10817}, {9669,10620}, {9672,10117}, {9919,10832}, {9984,10874}, {10066,11805}, {10798,12192}, {10833,12168}, {11376,11709}, {11393,12133}, {11502,12327}, {11871,12365}, {11872,12366}, {11906,12369}
X(12374) = reflection of X(10081) in X(496)
X(12374) = X(74)-of-2nd-Johnson-Yff-triangle
X(12374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,7728,12373), (3583,7727,265)
Let Ka, Kb, Kc be the free vertices of the Kenmotu squares. Triangle KaKbKc is here named the 1st Kenmotu free vertices triangle. KaKbKc is the anti-Kosnita triangle of the 1st Kenmotu diagonals triangle. KaKbKc is homothetic to ABC at X(372). X(12375) is the perspector of the 1st Kenmotu diagonals triangle and the reflection of KaKbKc in X(371). (Randy Hutson, July 21, 2017)
The reciprocal orthologic center of these triangles is X(3581).
X(12375) lies on these lines: {6,13}, {74,6200}, {110,372}, {125,10576}, {146,6561}, {371,5663}, {485,3448}, {590,10264}, {615,10272}, {1151,10620}, {1511,6396}, {1986,5412}, {2066,7727}, {2771,7969}, {3068,12317}, {3311,12308}, {5410,12165}, {5415,7724}, {5609,6420}, {6453,10817}, {7722,10880}, {7723,10897}, {7968,11699}, {8909,12302}, {9826,10961}, {11417,12219}, {11447,12270}, {11462,12281}, {11473,12292}, {11513,12358}
X(12375) = {X(6),X(399)}-harmonic conjugate of X(12376)
X(12375) = X(80)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(12375) = X(110)-of-1st-Kenmotu-free-vertices-triangle
The reciprocal orthologic center of these triangles is X(3581).
Let Ka', Kb', Kc' be the free vertices of the 2nd Kenmotu squares. Triangle Ka'Kb'Kc' is here named the 2nd Kenmotu free vertices triangle. Ka'Kb'Kc' is the anti-Kosnita triangle of the 2nd Kenmotu diagonals triangle. Ka'Kb'Kc' is homothetic to ABC at X(371). X(12376) is the perspector of the 2nd Kenmotu diagonals triangle and the reflection of Ka'Kb'Kc' in X(372). (Randy Hutson, July 21, 2017)
X(12376) lies on these lines: {6,13}, {74,6396}, {110,371}, {125,10577}, {146,6560}, {372,5663}, {486,3448}, {590,10272}, {615,10264}, {1152,10620}, {1511,6200}, {1986,5413}, {2771,7968}, {3069,12317}, {3312,12308}, {5411,12165}, {5414,7727}, {5416,7724}, {5609,6419}, {5642,8994}, {6126,8973}, {6454,10818}, {7722,10881}, {7723,10898}, {7969,11699}, {9826,10963}, {11418,12219}, {11448,12270}, {11463,12281}, {11474,12292}, {11514,12358}
X(12376) = {X(6),X(399)}-harmonic conjugate of X(12375)
X(12376) = X(80)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute
X(12376) = X(110)-of-2nd-Kenmotu-free-vertices-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12377) lies on these lines: {74,493}, {110,11828}, {113,8222}, {125,8212}, {146,6462}, {541,12152}, {690,12186}, {2777,9838}, {3028,11947}, {5663,10669}, {6461,12378}, {7725,8216}, {7726,8218}, {7728,8220}, {7978,8210}, {8188,9904}, {8194,9919}, {8214,12368}, {9984,10875}, {10065,11951}, {10081,11953}, {10620,11949}, {10945,12371}, {10951,12372}, {11377,11709}, {11394,12133}, {11503,12327}, {11840,12192}, {11846,12244}, {11907,12369}, {11930,12373}, {11932,12374}
X(12377) = X(74)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12378) lies on these lines: {74,494}, {110,11829}, {113,8223}, {125,8213}, {146,6463}, {541,12153}, {690,12187}, {2777,9839}, {3028,11948}, {5663,10673}, {6461,12377}, {7725,8217}, {7726,8219}, {7728,8221}, {7978,8211}, {8189,9904}, {8195,9919}, {8215,12368}, {9984,10876}, {10065,11952}, {10081,11954}, {10620,11950}, {10946,12371}, {10952,12372}, {11378,11709}, {11395,12133}, {11504,12327}, {11841,12192}, {11847,12244}, {11908,12369}, {11931,12373}, {11933,12374}
X(12378) = X(74)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(974).
X(12379) lies on these lines: {6,64}, {74,403}, {399,2935}, {974,10821}, {1656,3357}, {2777,3581}, {4550,10606}, {5663,12364}, {5895,11438}, {7687,10816}
The reciprocal orthologic center of these triangles is X(7731).
X(12380) lies on these lines: {6,24}, {23,12364}, {26,12280}, {74,10421}, {186,10821}, {399,1154}, {1495,2914}, {1614,6242}, {1657,7691}, {9707,12175}, {9920,11456}, {10628,12112}, {11438,12254}, {12290,12307}
X(12380) = reflection of X(2914) in X(1495)
X(12380) = {X(24), X(12291)}-harmonic conjugate of X(54)
The reciprocal orthologic center of these triangles is X(12112).
X(12381) lies on these lines: {1,74}, {12,12371}, {110,11248}, {113,5552}, {125,10531}, {146,10528}, {541,11239}, {690,12189}, {2777,12115}, {3028,10965}, {5663,10679}, {6256,10721}, {7725,10929}, {7726,10930}, {7728,10942}, {9919,10834}, {9984,10878}, {10620,12000}, {10803,12192}, {10805,12244}, {10915,12368}, {10955,12372}, {10956,12373}, {10958,12374}, {11400,12133}, {11509,12327}, {11881,12365}, {11882,12366}, {11914,12369}, {11955,12377}, {11956,12378}
X(12381) = reflection of X(74) in X(10065)
X(12381) = {X(74),X(7978)}-harmonic conjugate of X(12382)
X(12381) = X(74)-of-inner-Yff-tangents-triangle
The reciprocal orthologic center of these triangles is X(12112).
X(12382) lies on these lines: {1,74}, {11,12372}, {110,11249}, {113,10527}, {125,10532}, {146,10529}, {541,11240}, {690,12190}, {2777,12116}, {2779,10091}, {3028,10966}, {5663,10680}, {7725,10931}, {7726,10932}, {7728,10943}, {9919,10835}, {9984,10879}, {10620,12001}, {10804,12192}, {10806,12244}, {10916,12368}, {10949,12371}, {10957,12373}, {10959,12374}, {11401,12133}, {11510,12327}, {11883,12365}, {11884,12366}, {11915,12369}, {11957,12377}, {11958,12378}
X(12382) = reflection of X(74) in X(10081)
X(12382) = {X(74),X(7978)}-harmonic conjugate of X(12381)
X(12382) = X(74)-of-outer-Yff-tangents-triangle
Let A'B'C' be the dual of orthic triangle (a.k.a 1st anti-circumperp triangle). Let L, M, N be lines through A', B', C', respectively, parallel to the Euler line. Let L' be the reflection of L in sideline BC, and define M' and N' cyclically. The lines L', M', N' concur in X(12383). (cf. X(74), X(113), X(399), X(1511), X(5504), X(10692), X(14094), X(30714)) (Randy Hutson, March 21, 2019)
The reciprocal orthologic center of these triangles is X(6102).
X(12383) lies on the cubics K544, K611, K753 and these lines: {2,265}, {3,2888}, {4,110}, {20,5663}, {24,12310}, {30,146}, {67,10519}, {68,5963}, {69,74}, {100,12334}, {125,631}, {147,7422}, {185,12284}, {186,2931}, {193,1986}, {378,12168}, {381,10272}, {388,10088}, {497,10091}, {511,7731}, {515,2948}, {541,11001}, {550,2889}, {568,11561}, {974,2854}, {1092,12289}, {1112,7487}, {1503,2892}, {1539,3543}, {1656,11801}, {1657,12308}, {1993,2914}, {2771,3648}, {2777,3529}, {2781,5596}, {3028,4293}, {3060,11557}, {3068,10819}, {3069,10820}, {3090,5972}, {3091,10113}, {3146,5609}, {3520,12302}, {3522,12041}, {3524,6699}, {3533,6723}, {3545,5642}, {3564,10295}, {3567,11800}, {3616,12261}, {4302,7727}, {5055,11694}, {5157,5622}, {5562,12281}, {5603,11720}, {5648,11180}, {5656,11744}, {5667,9033}, {5889,11271}, {6053,10706}, {6143,12038}, {6193,7722}, {6560,12375}, {6561,12376}, {7552,11464}, {7706,11422}, {7732,10783}, {7733,10784}, {7787,12201}, {7967,7984}, {8907,9938}, {9919,12082}, {9927,11449}, {9934,11206}, {9976,11179}, {10114,11438}, {10117,12088}, {10574,11806}, {10628,11412}, {11469,12292}, {12270,12273}
X(12383) = midpoint of X(i) and X(j) for these {i,j}: {1657,12308}, {12270,12273}
X(12383) = reflection of X(i) in X(j) for these (i,j): (4,110), (20,12121), (146,399), (265,1511), (3146,7728), (3448,3), (3543,5655), (5889,11562), (7728,5609), (10620,550), (10733,113), (11180,5648), (12244,20), (12281,5562), (12284,185), (12317,74), (12319,5504)
X(12383) = isogonal conjugate of X(35372)
X(12383) = anticomplementary-circle-inverse of X(39118)
X(12383) = cevapoint of X(399) and X(2931)
X(12383) = crossdifference of every pair of points on line X(686)X(14398)
X(12383) = anticomplement of X(265)
X(12383) = X(265)-of-anticomplementary-triangle
X(12383) = X(110)-of-anti-Euler-triangle
X(12383) = crosspoint, wrt excentral or tangential triangle, of X(399) and X(2931)
X(12383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,5504,3043), (110,10733,113), (113,10733,4), (146,9143,399), (265,1511,2), (376,12317,74), (1147,12278,4)
The reciprocal orthologic center of these triangles is X(4).
X(12384) lies on the anticomplementary circle and these lines: {2,107}, {3,12253}, {4,339}, {20,112}, {100,12340}, {127,3091}, {146,9517}, {147,2799}, {148,2794}, {149,2831}, {150,2825}, {151,2853}, {152,9518}, {153,2806}, {388,6020}, {497,3320}, {2781,3448}, {3523,6720}, {3543,10735}, {3616,12265}, {3839,10718}, {5731,11722}, {7787,12207}
X(12384) = reflection of X(i) in X(j) for these (i,j): (20,112), (1297,132), (12253,3)
X(12384) = anticomplement of X(1297)
X(12384) = orthoptic circle of Steiner inellipse-inverse-of-X(6716)
X(12384) = polar circle-inverse-of-X(12145)
X(12384) = X(1297)-of-anticomplementary-triangle
X(12384) = X(12918)-of-anti-Euler-triangle
X(12384) = de-Longchamps-circle-inverse of X(34168)
X(12384) = {X(132), X(1297)}-harmonic conjugate of X(2)
The reciprocal orthologic center of these triangles is X(1).
X(12385) lies on these lines: {3,1279}, {10855,12386}
The reciprocal orthologic center of these triangles is X(1).
X(12386) lies on these lines: {10855,12385}, {10860,12387}
The reciprocal orthologic center of these triangles is X(1).
X(12387) lies on these lines: {3,1279}, {10860,12386}
The reciprocal orthologic center of these triangles is X(1).
X(12388) lies on these lines: {1,7056}, {3,1279}, {2961,7084}, {8583,12386}
X(12388) = reflection of X(12387) in X(3)
The reciprocal orthologic center of these triangles is X(1).
X(12389) lies on these lines: {100,12387}, {2975,12388}, {5744,12385}, {11678,12386}
The reciprocal orthologic center of these triangles is X(1).
X(12390) lies on these lines: {2,12385}, {21,12388}, {63,12389}, {7411,12387}, {10861,12386}
The reciprocal orthologic center of these triangles is X(1).
X(12391) lies on these lines: {7,12390}, {8,12386}, {329,12389}, {962,4645}, {3616,12388}, {9776,12385}, {9778,12387}
The reciprocal orthologic center of these triangles is X(1).
X(12392) lies on these lines: {1,5575}, {10434,12387}, {10444,12390}, {10446,12391}, {10856,12385}, {10862,12386}, {10882,12388}, {11679,12389}
The reciprocal orthologic center of these triangles is X(1).
X(12393) lies on these lines: {2,12387}, {4,12388}, {5,3823}, {8727,12385}, {9779,12391}, {10863,12386}, {10883,12390}, {10886,12392}, {11680,12389}
X(12393) = midpoint of X(4) and X(12388)
X(12393) = complement of X(12387)
The reciprocal orthologic center of these triangles is X(1).
X(12394) lies on these lines: {2,12388}, {4,12387}, {5,3823}, {10,1541}, {4197,12390}, {8582,12386}, {8728,12385}, {9780,12391}, {10887,12392}, {11681,12389}
X(12394) = midpoint of X(4) and X(12387)
X(12394) = reflection of X(12393) in X(5)
X(12394) = complement of X(12388)
The reciprocal orthologic center of these triangles is X(1).
X(12395) lies on these lines: {1,7056}, {145,12391}, {1721,7982}, {3679,12394}, {7991,12387}, {11518,12385}, {11519,12386}, {11520,12390}, {11521,12392}, {11522,12393}, {11682,12389}
X(12395) = midpoint of X(145) and X(12391)
X(12395) = reflection of X(7991) in X(12387)
The reciprocal orthologic center of these triangles is X(1).
X(12396) lies on these lines: {1,7056}, {2,12391}, {40,238}, {57,12385}, {63,12389}, {165,12387}, {1698,12394}, {1699,12393}, {1764,12392}, {8580,12386}
X(12396) = midpoint of X(12389) and X(12390)
X(12396) = reflection of X(i) in X(j) for these (i,j): (1,12388), (12395,1)
X(12396) = complement of X(12391)
X(12396) = Ursa-minor-to-excentral similarity image of X(17633)
The reciprocal orthologic center of these triangles is X(1).
X(12397) lies on these lines: {2,12385}, {4,341}, {9,12396}, {329,12389}, {405,12388}, {442,12394}, {5927,12386}, {7580,12387}, {8226,12393}, {10888,12392}, {11523,12395}
X(12397) = midpoint of X(12389) and X(12391)
X(12397) = reflection of X(12390) in X(12385)
X(12397) = anticomplement of X(12385)
X(12397) = complement of X(12390)
The reciprocal orthologic center of these triangles is X(1).
X(12398) lies on these lines: {1,5575}, {3,12396}, {20,12391}, {40,12387}, {78,12389}, {517,12395}, {1490,12397}, {3576,12388}, {5587,12394}, {8227,12393}, {8726,12385}, {10864,12386}, {10884,12390}
X(12398) = midpoint of X(20) and X(12391)
X(12398) = reflection of X(i) in X(j) for these (i,j): (40,12387), (12396,3)
The reciprocal orthologic center of these triangles is X(1).
X(12399) lies on these lines: {7,12390}, {9,12389}, {1445,12396}, {7675,12398}, {7676,12387}, {7677,12388}, {7678,12393}, {7679,12394}, {8232,12397}, {8732,12385}, {10865,12386}, {10889,12392}, {11526,12395}
X(12399) = reflection of X(12389) in X(9)
The reciprocal orthologic center of these triangles is X(1).
X(12400) lies on these lines: {1,5575}, {11,12394}, {12,12393}, {55,12388}, {56,12387}, {145,12389}, {950,12397}, {1697,12396}, {3601,12385}, {4313,12390}, {7962,12395}, {8236,12399}, {9785,12391}, {10866,12386}
X(12400) = midpoint of X(145) and X(12389)
The reciprocal orthologic center of these triangles is X(1).
X(12401) lies on these lines: {1,5575}, {495,12394}, {496,12393}, {942,12385}, {999,12388}, {3295,12387}, {3333,12396}, {3487,12397}, {3616,12389}, {11035,12386}, {11036,12390}, {11037,12391}, {11038,12399}, {11529,12395}
The reciprocal orthologic center of these triangles is X(1).
X(12402) lies on these lines: {1,5575}, {2,12389}, {7,12390}, {11,12393}, {12,12394}, {55,12387}, {56,12388}, {57,12385}, {226,12397}, {3340,12395}, {8581,12386}
X(12402) = midpoint of X(i) and X(j) for these {i,j}: {7,12399}, {12390,12391}
X(12402) = reflection of X(i) in X(j) for these (i,j): (1,12401), (12396,12385), (12400,1)
X(12402) = complement of X(12389)
The reciprocal orthologic center of these triangles is X(1).
X(12403) lies on these lines: {1,7056}, {57,12387}, {65,12400}, {226,12393}, {354,12402}, {1210,12394}, {3333,12398}, {3873,12389}, {5045,12401}, {5728,12397}, {10580,12391}, {11018,12385}, {11019,12386}, {11020,12390}, {11021,12392}, {11025,12399}
X(12403) = midpoint of X(65) and X(12400)
X(12403) = reflection of X(12401) in X(5045)
The reciprocal orthologic center of these triangles is X(1).
X(12404) lies on these lines: {1,5575}, {165,12387}, {200,12389}, {516,12391}, {1750,12397}, {3062,12386}, {4326,12399}, {5732,12390}, {7987,12388}, {7988,12393}, {7989,12394}, {10857,12385}, {10980,12403}, {11531,12395}
X(12404) = reflection of X(i) in X(j) for these (i,j): (1,12398), (11531,12395), (12396,12387)
The reciprocal orthologic center of these triangles is X(1).
X(12405) lies on these lines: {21,12388}, {846,12396}, {1284,12402}, {4199,12397}, {4220,12387}, {5051,12394}, {8229,12393}, {8235,12398}, {8238,12399}, {8240,12400}, {8245,12404}, {8246,12405}, {8731,12385}, {9791,12391}, {10868,12386}, {10892,12392}, {11031,12403}, {11043,12401}, {11533,12395}, {11688,12389}
X(12405) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13220)
The reciprocal orthologic center of these triangles is X(1).
X(12406) lies on these lines: {174,12402}, {7587,12388}, {8126,12389}, {8382,12394}, {8389,12399}, {8423,12404}, {8425,12405}, {8729,12385}, {11535,12395}, {11860,12386}, {11890,12390}, {11891,12391}, {11924,12400}
The reciprocal orthologic center of these triangles is X(6102).
X(12407) lies on these lines: {1,265}, {10,12383}, {30,9904}, {35,12334}, {110,5587}, {125,3576}, {165,12121}, {355,2948}, {381,11699}, {515,3448}, {542,3751}, {1511,1698}, {1699,10113}, {2777,9899}, {3028,9613}, {5663,5691}, {5886,11801}, {6264,10778}, {7713,12140}, {7724,8274}, {8227,11720}, {9140,11709}, {9578,10088}, {9581,10091}, {10789,12201}
X(12407) = reflection of X(i) in X(j) for these (i,j): (1,265), (2948,355), (6264,10778), (12383,10)
X(12407) = X(265)-of-Aquila-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12408) lies on the Bevan circle and these lines: {1,1297}, {10,12384}, {35,12340}, {57,6020}, {112,165}, {127,1699}, {132,1698}, {515,12253}, {1054,9527}, {1282,2825}, {1697,3320}, {1768,2806}, {2781,2948}, {2799,9860}, {2831,5541}, {3679,9530}, {5540,9523}, {7713,12145}, {7987,11722}, {9517,9904}, {10705,11531}, {10789,12207}
X(12408) = reflection of X(i) in X(j) for these (i,j): (1,1297), (11531,10705), (12384,10)
X(12408) = X(1297)-of-Aquila-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12409) lies on these lines: {1,5180}, {5,1768}, {35,12342}, {515,12255}, {7713,12146}, {10789,12209}
X(12409) = reflection of X(1) in X(10266)
X(12409) = X(10266)-of-Aquila-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12410) lies on these lines: {1,3}, {8,25}, {10,5020}, {22,145}, {23,3621}, {24,12245}, {26,5844}, {28,5082}, {42,1036}, {159,5846}, {197,3913}, {219,1973}, {355,1598}, {515,9910}, {518,3556}, {519,9798}, {859,1792}, {944,11414}, {946,11479}, {952,7387}, {958,1486}, {960,12329}, {961,4339}, {962,1593}, {970,7074}, {1037,1042}, {1398,4318}, {1610,3189}, {1616,5096}, {1995,3617}, {2802,9912}, {3220,6762}, {3421,4222}, {3434,4185}, {3435,8668}, {3436,4186}, {3616,7484}, {3622,7485}, {3623,6636}, {3632,8185}, {3633,9591}, {3871,11337}, {5247,7083}, {5250,7085}, {5603,7395}, {5690,6642}, {5790,7529}, {5901,7393}, {7465,10587}, {7509,10595}, {7516,10283}, {7967,10323}, {7978,12168}, {8132,11924}, {9780,11284}, {9812,11403}, {9956,11484}, {10046,10573}, {10790,12195}, {10829,10912}, {10833,10950}
X(12410) = X(8)-of-Ara-triangle
X(12410) = X(1)-of-3rd-antipedal-triangle-of-X(3)
X(12410) = orthologic center of these triangles: Ara to 2nd Schiffler
X(12410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,8193,3), (10,11365,5020), (22,145,8192)
The reciprocal orthologic center of these triangles is X(40).
X(12411) lies on these lines: {22,9874}, {24,12249}, {25,7160}, {197,12333}, {8000,8192}, {8185,9898}, {10037,10059}, {10046,10075}, {10790,12200}, {11365,12260}, {11414,12120}
X(12411) = X(7160)-of-Ara-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12412) lies on these lines: {3,74}, {6,11557}, {22,12383}, {24,3448}, {25,265}, {26,9920}, {30,9919}, {69,7502}, {113,9818}, {125,6642}, {146,378}, {155,10628}, {159,542}, {186,12317}, {197,12334}, {541,2935}, {1181,11562}, {1539,1597}, {1593,7728}, {1598,10113}, {1619,9934}, {1993,7731}, {2070,3580}, {2771,3556}, {2777,9914}, {2781,5504}, {3763,5621}, {5622,9826}, {5961,7669}, {5972,7393}, {6644,10264}, {7387,10117}, {7514,10272}, {8185,12407}, {9786,11806}, {10088,10831}, {10091,10832}, {10790,12201}, {11365,12261}, {11413,12244}, {11414,12121}, {12167,12236}
X(12412) = reflection of X(i) in X(j) for these (i,j): (7387,10117), (12085,12302), (12310,26)
X(12412) = circumcircle-inverse-of-X(12358)
X(12412) = X(265)-of-Ara-triangle
X(12412) = {X(74), X(110)}-harmonic conjugate of X(12358)
The reciprocal orthologic center of these triangles is X(4).
X(12413) lies on these lines: {3,132}, {22,12384}, {24,12253}, {25,1073}, {112,11414}, {127,1598}, {197,12340}, {1661,9530}, {2781,12310}, {2799,9861}, {2806,9913}, {3320,10833}, {7387,11641}, {8185,12408}, {9517,9919}, {10790,12207}, {11365,12265}
X(12413) = reflection of X(11641) in X(7387)
X(12413) = X(1297)-of-Ara-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12414) lies on these lines: {3,7701}, {24,12255}, {25,10266}, {197,12342}, {8185,12409}, {10790,12209}, {11365,12267}
X(12414) = X(10266)-of-Ara-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12415) lies on these lines: {55,12416}, {68,5597}, {155,8200}, {539,11207}, {1147,5599}, {3157,11869}, {5598,9933}, {5601,6193}, {8190,9908}, {8196,9927}, {8197,9928}, {10055,11877}, {10071,11879}, {11366,12259}, {11411,11843}, {11822,12118}, {11837,12193}
X(12415) = reflection of X(12416) in X(55)
X(12415) = X(68)-of-1st-Auriga-triangle
X(12415) = X(9933)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12416) lies on these lines: {55,12415}, {68,5598}, {155,8207}, {539,11208}, {1147,5600}, {3157,11870}, {5597,9933}, {5602,6193}, {8187,9896}, {8191,9908}, {8203,9927}, {8204,9928}, {10055,11878}, {11367,12259}, {11411,11844}, {11823,12118}, {11838,12193}
X(12416) = reflection of X(12415) in X(55)
X(12416) = X(68)-of-2nd-Auriga-triangle
X(12416) = X(9933)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(7387).
X(12417) lies on these lines: {19,155}, {40,9896}, {55,9931}, {65,921}, {68,71}, {1147,11428}, {2013,11460}, {2550,12318}, {3101,11411}, {3564,8141}, {5584,12301}, {6193,6197}, {7688,9938}, {8539,9926}, {9816,9820}, {9932,10902}, {10306,12309}, {10319,12359}, {10636,10659}, {10637,10660}, {11406,12166}, {11435,12235}, {11445,12271}, {11471,12293}
X(12417) = reflection of X(9931) in X(9937)
X(12417) = X(84)-of-extangents-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(9833).
X(12418) lies on the Jerabek hyperbola and these lines: {30,155}, {68,402}, {539,1651}, {1069,11906}, {1147,1650}, {3157,11905}, {4240,6193}, {9896,11852}, {9908,11853}, {9923,11885}, {9927,11897}, {9928,11900}, {9929,11901}, {9930,11902}, {9933,11910}, {10055,11912}, {10071,11913}, {11411,11845}, {11831,12259}, {11832,12134}, {11839,12193}, {11848,12328}, {11863,12415}, {11864,12416}
X(12418) = midpoint of X(4240) and X(6193)
X(12418) = reflection of X(i) in X(j) for these (i,j): (68,402), (1650,1147)
X(12418) = isogonal conjugate of X(13621)
X(12418) = X(68)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(1147).
X(12419) lies on these lines: {20,5663}, {25,10111}, {110,11585}, {159,542}, {265,403}, {1353,11566}, {1498,11744}, {1503,5504}, {3147,3448}, {6776,9826}
The reciprocal orthologic center of these triangles is X(12421).
X(12420) lies on these lines: {20,6193}, {26,159}, {68,3542}, {155,6146}, {186,11411}, {1147,3546}, {6623,9927}
X(12420) = X(4)-of-Aries-triangle
X(12420) = Aries-isogonal conjugate of X(32048)
The reciprocal orthologic center of these triangles is X(12420).
X(12421) lies on these lines: {5,6}, {378,11411}, {539,11802}, {1092,10257}, {1147,11245}, {5878,12293}, {6515,9908}, {9927,10151}, {12134,12235}
X(12421) = reflection of X(12134) in X(12235)
X(12421) = X(4)-of-2nd-Hyacinth-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12422) lies on these lines: {11,68}, {155,355}, {539,11235}, {912,1482}, {1147,1376}, {3157,9933}, {3434,6193}, {3564,10943}, {9896,10826}, {9908,10829}, {9923,10871}, {9927,10893}, {9928,10914}, {9929,10919}, {9930,10920}, {10055,10523}, {10071,10948}, {10785,11411}, {10794,12193}, {11373,12259}, {11390,12134}, {11826,12118}, {11865,12415}, {11866,12416}, {11903,12418}
X(12422) = reflection of X(12328) in X(1147)
X(12422) = reflection of X(12423) in X(155)
X(12422) = X(68)-of-inner-Johnson-triangle
X(12422) = X(12430)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12423) lies on these lines: {3,63}, {12,68}, {155,355}, {539,11236}, {958,1147}, {1069,9933}, {3436,6193}, {9896,10827}, {9908,10830}, {9923,10872}, {9927,10894}, {9929,10921}, {9930,10922}, {10055,10954}, {10071,10523}, {10786,11411}, {10795,12193}, {11374,12259}, {11391,12134}, {11500,12328}, {11827,12118}, {11867,12415}, {11868,12416}, {11904,12418}
X(12423) = reflection of X(12422) in X(155)
X(12423) = X(68)-of-outer-Johnson-triangle
X(12423) = X(12431)-of-inner-Johnson-triangle
The reciprocal orthologic center of these triangles is X(7387).
X(12424) lies on these lines: {6,1147}, {68,6413}, {155,5412}, {372,9932}, {1151,12301}, {2013,11462}, {2066,9931}, {3068,12318}, {3311,12309}, {3564,11265}, {5410,12166}, {5415,12417}, {6193,10880}, {6200,9938}, {9820,10961}, {11411,11417}, {11447,12271}, {11473,12293}, {11513,12359}
X(12424) = X(84)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(12424) = {X(6),X(9937)}-harmonic conjugate of X(12425)
The reciprocal orthologic center of these triangles is X(7387).
X(12425) lies on these lines: {6,1147}, {68,6414}, {155,5413}, {371,9932}, {1152,12301}, {2013,11463}, {3069,12318}, {3312,12309}, {3564,11266}, {5411,12166}, {5414,9931}, {5416,12417}, {6193,10881}, {6396,9938}, {9820,10963}, {11411,11418}, {11448,12271}, {11474,12293}, {11514,12359}
X(12425) = X(84)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute
X(12425) = {X(6),X(9937)}-harmonic conjugate of X(12424)
The reciprocal orthologic center of these triangles is X(9833).
X(12426) lies on these lines: {68,493}, {155,8220}, {539,12152}, {1147,8222}, {3157,11930}, {6193,6462}, {6461,12427}, {8188,9896}, {8194,9908}, {8210,9933}, {8212,9927}, {8214,9928}, {8216,9929}, {8218,9930}, {8408,9936}, {9923,10875}, {10055,11951}, {10071,11953}, {10945,12422}, {10951,12423}, {11377,12259}, {11394,12134}, {11411,11846}, {11503,12328}, {11828,12118}, {11840,12193}, {11907,12418}
X(12426) = X(68)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12427) lies on these lines: {68,494}, {155,8221}, {539,12153}, {1147,8223}, {3157,11931}, {6193,6463}, {6461,12426}, {8189,9896}, {8195,9908}, {8211,9933}, {8213,9927}, {8215,9928}, {8217,9929}, {8219,9930}, {8420,9936}, {9923,10876}, {10055,11952}, {10071,11954}, {10946,12422}, {10952,12423}, {11378,12259}, {11395,12134}, {11411,11847}, {11504,12328}, {11829,12118}, {11841,12193}, {11908,12418}
X(12427) = X(68)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12428) lies on these lines: {1,9931}, {3,10071}, {4,651}, {5,11429}, {11,1147}, {12,9927}, {30,7352}, {33,12134}, {35,12359}, {55,68}, {56,12118}, {155,1479}, {497,1069}, {539,3058}, {912,10572}, {1062,6146}, {1478,12293}, {1594,9637}, {1697,9896}, {1837,9928}, {2098,9933}, {2646,12259}, {3028,7354}, {3056,3564}, {3167,9669}, {3295,10055}, {4294,11411}, {4302,12163}, {5432,5449}, {5433,12038}, {5654,10896}, {7741,9820}, {9645,9833}, {9668,12164}, {9670,9936}, {9908,10833}, {9923,10877}, {9929,10927}, {9930,10928}, {10799,12193}, {10947,12422}, {10953,12423}, {11909,12418}, {11947,12426}, {11948,12427}
X(12428) = X(68)-of-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(9833).
X(12429) lies on these lines: {3,68}, {4,193}, {5,3167}, {6,10112}, {26,9920}, {30,11411}, {69,11821}, {155,195}, {382,6243}, {517,9896}, {542,1498}, {567,1147}, {568,12235}, {912,4018}, {999,10071}, {1069,9669}, {1216,11850}, {1352,11479}, {1503,9914}, {1593,11442}, {1598,12134}, {1657,10620}, {1993,7507}, {2013,12111}, {2888,7503}, {3060,11576}, {3157,9654}, {3295,10055}, {3448,11413}, {3515,3580}, {3526,5449}, {3527,7528}, {3534,7689}, {3542,8780}, {3575,6515}, {3843,9936}, {3851,5654}, {5050,7399}, {5054,12038}, {5055,9820}, {5489,8057}, {5562,11898}, {5790,9928}, {5889,12173}, {5907,8681}, {6238,9668}, {6776,6823}, {6815,11245}, {7352,9655}, {7383,12017}, {7395,12022}, {7517,9908}, {7544,9777}, {7592,8548}, {8909,8976}, {8912,8981}, {9301,9923}, {9818,12166}, {9825,11433}, {9833,9909}, {9929,11916}, {9930,11917}, {9933,10247}, {10246,12259}, {11459,12271}, {11842,12193}, {11849,12328}, {11875,12415}, {11876,12416}, {11911,12418}, {11928,12422}, {11929,12423}, {11949,12426}, {11950,12427}
X(12429) = midpoint of X(2013) and X(12111)
X(12429) = reflection of X(i) in X(j) for these (i,j): (3,68), (155,9927), (382,12293), (1657,12163), (6193,5), (12118,12359), (12164,4)
X(12429) = homothetic center of Ehrmann side-triangle and X3-ABC reflections triangle
X(12429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (68,12118,12359), (155,9927,381), (1352,12241,11479), (10055,12428,3295), (12118,12359,3)
The reciprocal orthologic center of these triangles is X(9833).
X(12430) lies on these lines: {1,68}, {12,12422}, {119,5654}, {155,10942}, {539,11239}, {952,1854}, {1069,10958}, {1147,5552}, {3157,10956}, {6193,10528}, {9908,10834}, {9923,10878}, {9927,10531}, {9928,10915}, {9929,10929}, {9930,10930}, {10803,12193}, {10805,11411}, {10955,12423}, {10965,12428}, {11248,12118}, {11400,12134}, {11509,12328}, {11881,12415}, {11882,12416}, {11914,12418}, {11955,12426}, {11956,12427}, {12000,12429}
X(12430) = reflection of X(68) in X(10055)
X(12430) = X(68)-of-inner-Yff-tangents-triangle
X(12430) = {X(68),X(9933)}-harmonic conjugate of X(12431)
The reciprocal orthologic center of these triangles is X(9833).
X(12431) lies on these lines: {1,68}, {11,12423}, {155,10943}, {539,11240}, {912,1479}, {1069,10959}, {1147,10527}, {3157,10957}, {6193,10529}, {9908,10835}, {9923,10879}, {9927,10532}, {9928,10916}, {9929,10931}, {9930,10932}, {10804,12193}, {10806,11411}, {10949,12422}, {10966,12428}, {11249,12118}, {11401,12134}, {11510,12328}, {11883,12415}, {11884,12416}, {11915,12418}, {11957,12426}, {11958,12427}, {12001,12429}
X(12431) = reflection of X(68) in X(10071)
X(12431) = X(68)-of-outer-Yff-tangents-triangle
X(12431) = {X(68),X(9933)}-harmonic conjugate of X(12430)
Let A'B'C' be the orthic triangle of a triangle ABC. Let (Oa) be the incircle of AB'C', and define (Ob) and (Oc) cyclically. Then X(12432) = radical center of (Oa), (Ob), (Oc); see figure 1 and figure 2 . (Contributed by Thanh Oai Dao, March 4, 2017)
X(12432) lies on these lines: {1,1170}, {6,4347}, {7,5904}, {10,12}, {35,10122}, {46,10884}, {56,3881}, {57,3811}, {200,3339}, {201,3743}, {517,6738}, {518,4298}, {653,1844}, {942,6684}, {960,6666}, {962,1479}, {1125,5173}, {1203,4318}, {1254,3293}, {1400,3970}, {1420,3892}, {1448,3751}, {1708,5248}, {1724,4332}, {1788,5883}, {1825,1873}, {1902,5185}, {2099,3884}, {2171,3294}, {2800,6797}, {2801,4292}, {3085,5902}, {3256,7098}, {3305,3869}, {3340,3878}, {3361,3873}, {3485,10176}, {3555,4315}, {3681,5290}, {4294,10399}, {4314,5728}, {5435,5442}, {5884,11500}, {5905,12059}
X(12432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (65,72,3671), (65,4848,3754), (3678,3754,3841), (5728,7957,4314).
Let A'B'C' be the orthic triangle of a triangle ABC. Let (Oa) be the incircle of AB'C', and define (Ob) and (Oc) cyclically. Then X(12433) = center of the circle that is externally tangent to (Oa), (Ob), (Oc); i.e., the outer Apollonian circle of (Oa), (Ob), (Oc), which passes through X(12019). See figure 1 and figure 2 , (Contributed by Thanh Oai Dao, March 4, 2017)
Let A'B'C' be the orthic triangle. Let Oa be the circle centered at A' and tangent to the internal angle bisector of angle A, and define Ob and Oc cyclically. Then X(12433) is the radical center of circles Oa, Ob, Oc. (Angel Montesdeoca, August 31, 2019)
X(12433) lies on these lines: {1,5}, {3,938}, {4,6147}, {7,382}, {8,5284}, {20,5708}, {30,553}, {36,10543}, {40,10386}, {57,550}, {140,1210}, {145,3940}, {226,546}, {354,10572}, {381,3487}, {404,9945}, {452,3927}, {515,5045}, {517,6738}, {519,4015}, {528,3754}, {529,3881}, {548,4304}, {549,3601}, {944,5804}, {962,1159}, {999,3486}, {1056,6849}, {1058,1482}, {1385,11019}, {1656,5703}, {1844,1852}, {1895,7510}, {2095,6868}, {2310,5492}, {2829,12005}, {3058,5903}, {3189,9709}, {3244,3452}, {3295,5690}, {3303,10573}, {3337,5441}, {3419,8728}, {3475,9654}, {3485,9669}, {3526,5704}, {3530,3911}, {3579,4314}, {3583,3649}, {3586,3627}, {3622,6856}, {3623,6919}, {3626,6666}, {3632,7308}, {3748,10039}, {3811,3820}, {3843,5714}, {3845,9612}, {3851,5226}, {3868,11113}, {3884,5855}, {4295,9668}, {4299,4860}, {4302,5221}, {4342,11278}, {4857,5425}, {4995,5445}, {5049,10106}, {5253,10609}, {5274,6866}, {5436,5791}, {5572,7686}, {5728,5762}, {5761,10247}, {5790,6887}, {5818,10578}, {5840,5885}, {5841,6583}, {5844,9957}, {5882,7682}, {5902,6284}, {6261,7956}, {6675,6734}, {6825,10246}, {6844,10595}, {6848,7967}, {8148,9785}, {10051,11510}, {11544,11551}
X(12433) = midpoint of X(942) and X(950)
X(12433) = reflection of X(5045) in X(6744)
X(12433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5,5719), (1,11,37737), (1,496,5901), (1,1837,495), (1,5722,5), (1,9581,11374), (1,11373,10283), (145,5084,3940), (938,3488,3), (944,10580,7373), (1482,6827,5763), (5722,11374,9581), (9581,11374,5), (9785,11041,8148)
Orthologic centers: X(12434)-X(12624)
Centers X(12434)-X(12624) were contributed by César Eliud Lozada, March, 22, 2017.
The reciprocal orthologic center of these triangles is X(2).
X(12434) lies on the Artzt circle and these lines: {2,12157}, {98,512}, {111,9831}, {263,2679}, {511,9877}
X(12434) = circumsymmedial-to-Artzt similarity image of X(2698)
The reciprocal orthologic center of these triangles is X(942).
X(12435) lies on these lines: {1,3}, {8,10435}, {10,10478}, {63,10451}, {72,10888}, {145,10465}, {511,5691}, {516,10454}, {518,10442}, {519,12126}, {946,10479}, {962,10449}, {970,1698}, {975,994}, {2292,10892}, {3216,9549}, {3632,10825}, {3741,4301}, {3868,10444}, {3869,11679}, {5587,5752}, {5836,10456}, {7672,10889}, {8093,11894}, {9780,10440}, {9808,10891}
X(12435) = reflection of X(1) in X(10441)
X(12435) = Conway circle-inverse-of-X(1319)
X(12435) = X(4)-of-3rd-Conway-triangle
X(12435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,40,10434), (1,165,10470), (1,1764,10882), (1,10441,10439), (10,10478,10887), (55,10474,1), (65,10480,1), (946,10479,10886), (1764,11521,1), (2098,10475,1), (3057,10473,1), (7982,10476,1), (10446,10447,10435)
The reciprocal orthologic center of these triangles is X(1).
X(12436) lies on these lines: {1,6904}, {2,4292}, {3,142}, {4,5437}, {5,6692}, {7,936}, {10,57}, {20,10857}, {58,3008}, {72,553}, {84,6864}, {140,3824}, {226,474}, {376,5436}, {377,1210}, {386,3664}, {404,5249}, {442,3911}, {515,3812}, {519,942}, {527,5044}, {535,11575}, {551,3601}, {758,10855}, {950,5439}, {975,3663}, {997,3671}, {1054,5530}, {1056,1706}, {1329,3634}, {1467,4315}, {1478,8582}, {1698,5744}, {1770,3624}, {2095,11362}, {2550,3333}, {2999,4340}, {3243,3296}, {3244,11518}, {3338,4847}, {3361,8732}, {3487,5438}, {3600,9623}, {3616,10624}, {3626,5708}, {3646,5698}, {3678,5850}, {3698,5434}, {3752,5717}, {3753,10106}, {3811,5542}, {3817,6847}, {3825,8727}, {3828,5791}, {3833,11227}, {3838,6691}, {3874,6743}, {3922,10944}, {4190,4304}, {4208,5435}, {4255,4675}, {4294,10582}, {4295,8583}, {4297,8726}, {4301,6282}, {4355,8580}, {4413,10404}, {4511,9782}, {5045,5853}, {5084,9579}, {5087,5122}, {5691,11407}, {5715,6926}, {5883,6738}, {5902,6737}, {6245,6256}, {6259,9842}, {6260,6918}, {6678,6693}, {6744,11018}, {6765,11037}, {6824,10171}, {6849,7171}, {6850,7682}, {6935,8227}, {7330,8257}, {10164,10198}
X(12436) = midpoint of X(i) and X(j) for these {i,j}: {10,4298}, {3874,6743}
X(12436) = X(389)-of-Ascella-triangle
X(12436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,142,1125), (4,5437,9843), (57,443,10), (226,474,6700), (377,3306,1210), (3600,11024,9623), (4208,5435,5705), (5438,6173,3487), (5439,11112,950), (5745,8728,3634), (6904,9776,1)
The reciprocal orthologic center of these triangles is X(1).
X(12437) lies on these lines: {1,142}, {3,519}, {8,3158}, {9,4313}, {10,6675}, {20,527}, {21,5325}, {55,5837}, {57,145}, {72,4304}, {78,950}, {100,4848}, {200,3486}, {210,10543}, {226,2475}, {284,1043}, {515,3811}, {517,9942}, {518,4297}, {522,5592}, {528,4301}, {551,3813}, {553,4190}, {579,3169}, {936,3488}, {938,5438}, {942,3244}, {944,6282}, {952,6245}, {958,6600}, {960,4314}, {1210,5440}, {1265,2325}, {1376,6738}, {1483,9940}, {1837,6745}, {2646,4847}, {2802,9946}, {3241,3680}, {3243,3600}, {3522,3928}, {3555,4311}, {3621,5744}, {3626,5791}, {3679,6857}, {3689,6736}, {3870,10106}, {3879,7176}, {3911,4855}, {3939,5247}, {3984,6872}, {4035,7270}, {4320,8271}, {4511,12053}, {4685,8731}, {5175,5219}, {5436,6666}, {5720,9842}, {5722,6700}, {5727,7080}, {5730,10624}, {5731,6762}, {5836,11018}, {5854,9945}, {5881,6847}, {6049,8732}, {7967,8726}, {9843,12433}, {10165,10916}, {10857,11519}
X(12437) = midpoint of X(i) and X(j) for these {i,j}: {1,3189}, {20,11523}, {145,2136}, {944,6765}, {3243,7674}
X(12437) = reflection of X(i) in X(j) for these (i,j): (10912,3635), (11362,8715)
X(12437) = orthologic center of these triangles: Ascella to 2nd Schiffler
X(12437) = X(64)-of-Ascella-triangle
X(12437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8,3601,5745), (55,6737,5837), (78,950,3452), (200,3486,5795), (938,5438,6692), (3241,6904,11518), (3555,10609,4311), (3689,10950,6736), (4190,11520,553)
The reciprocal orthologic center of these triangles is X(3).
X(12438) lies on these lines: {1,402}, {3,11848}, {8,4240}, {10,1650}, {30,40}, {55,11863}, {515,12113}, {517,11251}, {519,1651}, {944,11845}, {946,11897}, {1482,11911}, {1829,11832}, {1837,11906}, {3057,11909}, {3081,4669}, {3640,11902}, {3641,11901}, {5252,11905}, {9798,11853}, {9941,11885}, {11839,12194}
X(12438) = midpoint of X(i) and X(j) for these {i,j}: {8,4240}, {11903,11904}
X(12438) = reflection of X(i) in X(j) for these (i,j): (1,402), (1650,10), (11831,11852)
X(12438) = X(1)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(3555).
X(12439) lies on these lines: {3,12333}, {142,5045}, {518,12260}, {3555,7160}, {3601,5920}, {3889,9874}, {8001,10857}, {9776,9804}, {9953,10855}
X(12439) = midpoint of X(3555) and X(7160)
The reciprocal orthologic center of these triangles is X(3).
X(12440) lies on these lines: {1,493}, {3,11503}, {8,6462}, {40,11828}, {55,8201}, {355,8220}, {515,9838}, {517,10669}, {519,12152}, {944,11846}, {946,8212}, {1482,11949}, {1829,11394}, {1837,11932}, {2292,8393}, {3057,11947}, {3640,8218}, {3641,8216}, {5252,11930}, {6339,8215}, {6461,12441}, {8194,9798}, {9941,10875}, {11840,12194}, {11907,12438}
X(12440) = X(1)-of-Lucas-homothetic-triangle
X(12440) = {X(8201),X(8208)}-harmonic conjugate of X(55)
The reciprocal orthologic center of these triangles is X(3).
X(12441) lies on these lines: {1,494}, {3,11504}, {8,6463}, {10,8223}, {40,11829}, {55,8202}, {355,8221}, {515,9839}, {517,10673}, {519,12153}, {944,11847}, {946,8213}, {1482,11950}, {1829,11395}, {1837,11933}, {2292,8394}, {3057,11948}, {3640,8219}, {3641,8217}, {5252,11931}, {6339,8214}, {6461,12440}, {8195,9798}, {9941,10876}, {11841,12194}, {11908,12438}
X(12441) = X(1)-of-Lucas(-1)-homothetic-triangle
X(12441) = {X(8202),X(8209)}-harmonic conjugate of X(55)
The reciprocal orthologic center of these triangles is X(3555).
X(12442) lies on these lines: {2,12538}, {3,12517}, {5744,12534}, {8727,12613}, {8728,12621}, {9776,12542}, {10855,12449}, {10856,12553}
The reciprocal orthologic center of these triangles is X(1).
X(12443) lies on these lines: {1,8733}, {57,164}, {167,10857}, {3601,8422}, {5571,11018}, {5744,11691}, {7670,8732}, {9776,9807}
X(12443) = orthologic center of these triangles: Ascella to 2nd midarc
X(12443) = X(1)-of-Ascella-triangle
X(12443) = {X(8733),X(8734)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(21).
X(12444) lies on these lines: {3,12342}, {226,2475}, {942,3838}, {6841,9946}
The reciprocal orthologic center of these triangles is X(942).
X(12445) lies on these lines: {10,8382}, {57,7588}, {65,174}, {258,3339}, {517,8130}, {519,12130}, {2292,8425}, {3057,10502}, {3868,11890}, {3869,8126}, {5902,11217}, {7672,8389}, {7991,8423}, {9808,11996}, {11896,12435}
X(12445) = {X(3057), X(10502)}-harmonic conjugate of X(11924)
The reciprocal orthologic center of these triangles is X(1).
X(12446) lies on these lines: {1,9859}, {8,79}, {10,5927}, {516,960}, {1125,10855}, {3062,5234}, {3555,3671}, {3841,6702}, {3878,9589}, {3884,10624}, {4301,5784}, {4314,10609}, {5248,8583}, {6001,9947}
X(12446) = X(578)-of-Atik-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12447) lies on these lines: {1,2}, {3,9948}, {9,4297}, {20,3062}, {72,4298}, {210,10106}, {220,5783}, {392,10866}, {405,10392}, {443,3671}, {515,5044}, {516,960}, {518,11035}, {553,3962}, {758,10855}, {993,8273}, {1001,12437}, {1376,5837}, {1706,6766}, {1837,5316}, {2550,4301}, {3035,9952}, {3160,5232}, {3452,5794}, {3488,3646}, {3600,5223}, {3678,9954}, {3740,5795}, {3874,10569}, {3876,11678}, {3878,7957}, {3923,9950}, {3983,10944}, {4005,5434}, {4292,5692}, {4308,5686}, {4314,10384}, {4342,5082}, {4413,4848}, {5234,5731}, {5273,7987}, {5328,7989}, {5438,10164}, {5542,11523}, {5791,10165}, {5833,11036}, {5882,9708}, {5927,10176}, {8158,9709}, {9858,9943}, {9949,10860}
X(12447) = midpoint of X(i) and X(j) for these {i,j}: {1,6743}, {72,4298}, {6737,6738}
X(12447) = reflection of X(6744) in X(1125)
X(12447) = complement of X(6738)
X(12447) = X(389)-of-Atik-triangle
X(12447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,3632,9797), (2,6737,6738), (8,8580,10), (8,8583,11019), (10,997,1125), (10,3244,9623), (10,6700,3634), (1125,3626,10916), (8583,11019,1125)
The reciprocal orthologic center of these triangles is X(1).
X(12448) lies on these lines: {8,210}, {145,8581}, {517,9948}, {518,3062}, {519,9856}, {2136,8580}, {2802,9952}, {3244,11035}, {3340,10912}, {3621,11678}, {3813,8582}, {3878,9953}, {3913,8583}, {4853,10384}, {5836,11019}, {5854,9951}, {9957,12447}, {10178,11260}, {10855,12437}
X(12448) = orthologic center of these triangles: Atik to 2nd Schiffler
X(12448) = X(64)-of-Atik-triangle
The reciprocal orthologic center of these triangles is X(3555).
X(12449) lies on these lines: {8,12542}, {8582,12621}, {8583,12522}, {10855,12442}, {10860,12517}, {10861,12538}, {10862,12553}, {10863,12613}, {11678,12534}
The reciprocal orthologic center of these triangles is X(1).
X(12450) lies on these lines: {1,9853}, {8,9807}, {164,8580}, {167,3062}, {177,8581}, {5571,11019}, {7670,10865}, {8422,10866}, {10855,12443}, {11678,11691}
X(12450) = orthologic center of these triangles: Atik to 2nd midarc
X(12450) = X(1)-of-Atik-triangle
X(12450) = {X(11858),X(11859)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(21).
X(12451) lies on these lines: {8,10266}, {3062,6597}, {10855,12444}
The reciprocal orthologic center of these triangles is X(3).
X(12452) lies on these lines: {6,5597}, {55,63}, {69,5601}, {141,5599}, {159,8190}, {511,11252}, {524,11207}, {611,11877}, {613,11879}, {1350,11822}, {1351,11875}, {1352,8200}, {1386,11366}, {1843,11384}, {2781,12365}, {3056,11873}, {3094,11861}, {3242,5598}, {3416,8197}, {3564,12415}, {5480,8196}, {6776,11843}, {9041,11208}, {9830,12345}, {11492,12329}, {11837,12212}
X(12452) = reflection of X(12453) in X(55)
X(12452) = {X(8198),X(8199)}-harmonic conjugate of X(5597)
X(12452) = X(6)-of-1st-Auriga-triangle
X(12452) = X(3242)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12453) lies on these lines: {6,5598}, {55,63}, {69,5602}, {141,5600}, {159,8191}, {511,11253}, {524,11208}, {611,11878}, {613,11880}, {1350,11823}, {1351,11876}, {1352,8207}, {1386,11367}, {1843,11385}, {3056,11874}, {3094,11862}, {3242,5597}, {3416,8204}, {3564,12416}, {3751,8187}, {5480,8203}, {6776,11844}, {9041,11207}, {9830,12346}, {11493,12329}, {11838,12212}
X(12453) = reflection of X(12452) in X(55)
X(12453) = {X(8205),X(8206)}-harmonic conjugate of X(5598)
X(12453) = X(6)-of-2nd-Auriga-triangle
X(12453) = X(3242)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12454) lies on these lines: {1,5599}, {8,5597}, {10,11366}, {55,519}, {145,5598}, {355,8196}, {944,11822}, {1482,8200}, {2098,11871}, {2099,11869}, {3244,11367}, {3621,5602}, {3633,8187}, {3913,11492}, {5844,11253}, {5846,12452}, {8190,12410}, {8207,11875}, {9053,12453}, {10573,11879}, {10912,11865}, {10950,11873}, {11384,12135}, {11823,11843}, {11837,12195}
X(12454) = X(12454) = reflection of X(i) in X(j) for these (i,j): (11208,11207), (12455,55)
X(12454) = X(8)-of-1st-Auriga-triangle
X(12454) = X(145)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12455) lies on these lines: {1,5600}, {8,5598}, {10,11367}, {55,519}, {145,5597}, {355,8203}, {944,11823}, {1482,8196}, {2098,11872}, {2099,11870}, {3244,11366}, {3621,5601}, {3632,8187}, {3913,11493}, {5844,11252}, {5846,12453}, {8191,12410}, {8200,11876}, {9053,12452}, {10573,11880}, {10912,11866}, {10950,11874}, {11385,12135}, {11822,11844}, {11838,12195}
X(12455) = reflection of X(i) in X(j) for these (i,j): (11207,11208), (12454,55)
X(12455) = X(8)-of-2nd-Auriga-triangle
X(12455) = X(145)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12456) lies on these lines: {55,6001}, {84,5597}, {515,12454}, {971,11252}, {1490,11822}, {1709,11877}, {5598,7971}, {5599,6260}, {6245,8196}, {6257,8199}, {6258,8198}, {6259,8200}, {8190,9910}, {10085,11879}, {11366,12114}, {11492,12330}, {11837,12196}, {11843,12246}
X(12456) = reflection of X(12457) in X(55)
X(12456) = X(84)-of-1st-Auriga-triangle
X(12456) = X(7971)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12457) lies on these lines: {55,6001}, {84,5598}, {515,12455}, {971,11253}, {1490,11823}, {1709,11878}, {5597,7971}, {5600,6260}, {6245,8203}, {6257,8206}, {6258,8205}, {6259,8207}, {7992,8187}, {8191,9910}, {10085,11880}, {11367,12114}, {11493,12330}, {11838,12196}, {11844,12246}
X(12457) = reflection of X(12456) in X(55)
X(12457) = X(84)-of-2nd-Auriga-triangle
X(12457) = X(7971)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12458) lies on these lines: {1,3}, {4,8197}, {10,8196}, {515,12454}, {946,5599}, {962,5601}, {1836,11869}, {2800,12457}, {4301,8203}, {5600,11362}, {5812,11867}, {6361,11843}, {8190,9911}, {8204,12245}, {11837,12197}
X(12458) = reflection of X(i) in X(j) for these (i,j): (55,11252), (12459,55)
X(12458) = X(40)-of-1st-Auriga-triangle
X(12458) = X(7982)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12459) lies on these lines: {1,3}, {4,8204}, {10,8203}, {515,12455}, {946,5600}, {962,5602}, {1836,11870}, {2800,12456}, {4301,8196}, {5599,11362}, {5812,11868}, {6361,11844}, {8191,9911}, {8197,12245}, {11838,12197}
X(12459) = reflection of X(i) in X(j) for these (i,j): (55,11253), (12458,55)
X(12459) = X(40)-of-2nd-Auriga-triangle
X(12459) = X(7982)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12460) lies on these lines: {11,11366}, {55,952}, {80,5597}, {100,8197}, {214,5599}, {1317,11367}, {2802,12454}, {2829,12456}, {5598,7972}, {5601,6224}, {5840,12458}, {6262,8199}, {6263,8198}, {6265,8200}, {8190,9912}, {10057,11877}, {10073,11879}, {11384,12137}, {11492,12331}, {11822,12119}, {11837,12198}, {11843,12247}
X(12460) = reflection of X(12461) in X(55)
X(12460) = X(80)-of-1st-Auriga-triangle
X(12460) = X(7972)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12461) lies on these lines: {11,11367}, {55,952}, {80,5598}, {100,8204}, {214,5600}, {1317,11366}, {2802,12455}, {2829,12457}, {5597,7972}, {5602,6224}, {5840,12459}, {6262,8206}, {6263,8205}, {6265,8207}, {8187,9897}, {8191,9912}, {10057,11878}, {10073,11880}, {11385,12137}, {11493,12331}, {11823,12119}, {11838,12198}, {11844,12247}
X(12461) = reflection of X(12460) in X(55)
X(12461) = X(80)-of-2nd-Auriga-triangle
X(12461) = X(7972)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12462) lies on these lines: {11,8196}, {55,2800}, {100,11822}, {104,5597}, {119,5599}, {153,5601}, {515,12460}, {1317,11873}, {1537,8203}, {2787,12179}, {2802,12458}, {5598,10698}, {8190,9913}, {10058,11877}, {10074,11879}, {11366,11715}, {11492,12332}, {11837,12199}, {11843,12248}
X(12462) = reflection of X(12463) in X(55)
X(12462) = X(104)-of-1st-Auriga-triangle
X(12462) = X(10698)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12463) lies on these lines: {11,8203}, {55,2800}, {100,11823}, {104,5598}, {119,5600}, {153,5602}, {515,12461}, {1317,11874}, {1537,8196}, {1768,8187}, {2787,12180}, {2802,12459}, {5597,10698}, {8191,9913}, {10058,11878}, {10074,11880}, {11367,11715}, {11493,12332}, {11838,12199}, {11844,12248}
X(12463) = reflection of X(12462) in X(55)
X(12463) = X(104)-of-2nd-Auriga-triangle
X(12463) = X(10698)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12464) lies on these lines: {55,12465}, {5597,7160}, {5598,8000}, {5601,9874}, {8190,12411}, {10059,11877}, {10075,11879}, {11366,12260}, {11492,12333}, {11822,12120}, {11837,12200}, {11843,12249}
X(12464) = reflection of X(12465) in X(55)
X(12464) = X(7160)-of-1st-Auriga-triangle
X(12464) = X(8000)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12465) lies on these lines: {55,12464}, {5597,8000}, {5598,7160}, {5602,9874}, {8187,9898}, {8191,12411}, {10059,11878}, {10075,11880}, {11367,12260}, {11493,12333}, {11823,12120}, {11838,12200}, {11844,12249}
X(12465) = reflection of X(12464) in X(55)
X(12465) = X(7160)-of-2nd-Auriga-triangle
X(12465) = X(8000)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12466) lies on these lines: {30,12365}, {55,12467}, {110,8200}, {542,12452}, {1511,5599}, {3448,11843}, {5601,12383}, {11822,12121}
X(12466) = reflection of X(12467) in X(55)
X(12466) = X(265)-of-1st-Auriga-triangle
X(12466) = X(12898)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12467) lies on these lines: {30,12366}, {55,12466}, {110,8207}, {542,12453}, {1511,5600}, {2771,12461}, {3448,11844}, {5602,12383}, {8187,12407}, {8191,12412}, {10091,11872}, {11367,12261}, {11493,12334}, {11823,12121}, {11838,12201}
X(12467) = reflection of X(12466) in X(55)
X(12467) = X(265)-of-2nd-Auriga-triangle
X(12467) = X(12898)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12468) lies on these lines: {30,12415}, {55,12469}, {64,5597}, {1498,11822}, {2777,12466}, {2883,5599}, {5598,7973}, {5601,6225}, {5878,8200}, {6000,11252}, {6001,12458}, {6247,8196}, {6266,8199}, {6267,8198}, {7355,11873}, {8190,9914}, {10060,11877}, {10076,11879}, {11366,12262}, {11381,11384}, {11492,12335}, {11837,12202}, {11843,12250}
X(12468) = reflection of X(12469) in X(55)
X(12468) = X(64)-of-1st-Auriga-triangle
X(12468) = X(7973)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12469) lies on these lines: {30,12416}, {55,12468}, {64,5598}, {1498,11823}, {2777,12467}, {2883,5600}, {5597,7973}, {5602,6225}, {5878,8207}, {6000,11253}, {6001,12459}, {6247,8203}, {6266,8206}, {6267,8205}, {7355,11874}, {8187,9899}, {8191,9914}, {10060,11878}, {10076,11880}, {11367,12262}, {11381,11385}, {11493,12335}, {11838,12202}, {11844,12250}
X(12469) = reflection of X(12468) in X(55)
X(12469) = X(64)-of-2nd-Auriga-triangle
X(12469) = X(7973)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12470) lies on these lines: {14,5597}, {55,12471}, {530,12345}, {531,11207}, {542,12452}, {617,5601}, {619,5599}, {5474,11822}, {5479,8196}, {5598,7974}, {5613,8200}, {6269,8199}, {6271,8198}, {6773,11843}, {9981,11861}, {10061,11877}, {10077,11879}, {11366,11706}, {11492,12336}, {11837,12204}
X(12470) = reflection of X(12471) in X(55)
X(12470) = X(14)-of-1st-Auriga-triangle
X(12470) = X(7974)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12471) lies on these lines: {14,5598}, {55,12470}, {530,12346}, {531,11208}, {542,12453}, {617,5602}, {619,5600}, {5474,11823}, {5479,8203}, {5597,7974}, {5613,8207}, {6269,8206}, {6271,8205}, {6773,11844}, {8187,9900}, {9981,11862}, {10061,11878}, {10077,11880}, {11367,11706}, {11493,12336}, {11838,12204}
X(12471) = reflection of X(12470) in X(55)
X(12471) = X(14)-of-2nd-Auriga-triangle
X(12471) = X(7974)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12472) lies on these lines: {13,5597}, {55,12473}, {530,11207}, {531,12345}, {542,12452}, {616,5601}, {618,5599}, {5473,11822}, {5478,8196}, {5598,7975}, {5617,8200}, {6268,8199}, {6270,8198}, {6770,11843}, {9982,11861}, {10062,11877}, {10078,11879}, {11366,11705}, {11492,12337}, {11837,12205}
X(12472) = reflection of X(12473) in X(55)
X(12472) = X(13)-of-1st-Auriga-triangle
X(12472) = X(7975)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12473) lies on these lines: {13,5598}, {55,12472}, {530,11208}, {531,12346}, {542,12453}, {616,5602}, {618,5600}, {5473,11823}, {5478,8203}, {5597,7975}, {5617,8207}, {6268,8206}, {6270,8205}, {6770,11844}, {8187,9901}, {9982,11862}, {10062,11878}, {10078,11880}, {11367,11705}, {11493,12337}, {11838,12205}
X(12473) = reflection of X(12472) in X(55)
X(12473) = X(13)-of-2nd-Auriga-triangle
X(12473) = X(7975)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12474) lies on these lines: {39,5599}, {55,730}, {76,5597}, {194,5601}, {384,11837}, {538,11207}, {732,12452}, {2782,11252}, {3095,8200}, {5598,7976}, {5969,12345}, {6248,8196}, {6272,8199}, {6273,8198}, {8190,9917}, {9983,11861}, {10063,11877}, {10079,11879}, {11257,11822}, {11366,12263}, {11384,12143}, {11492,12338}, {11843,12251}
X(12474) = reflection of X(12475) in X(55)
X(12474) = X(76)-of-1st-Auriga-triangle
X(12474) = X(7976)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12475) lies on these lines: {39,5600}, {55,730}, {76,5598}, {194,5602}, {384,11838}, {538,11208}, {732,12453}, {2782,11253}, {3095,8207}, {5597,7976}, {5969,12346}, {6248,8203}, {6272,8206}, {6273,8205}, {8187,9902}, {8191,9917}, {9983,11862}, {10063,11878}, {10079,11880}, {11257,11823}, {11367,12263}, {11385,12143}, {11493,12338}, {11844,12251}
X(12475) = reflection of X(12474) in X(55)
X(12475) = X(76)-of-2nd-Auriga-triangle
X(12475) = X(7976)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12476) lies on these lines: {55,12477}, {83,5597}, {732,12452}, {754,11207}, {2896,5601}, {5598,7977}, {5599,6292}, {6249,8196}, {6274,8199}, {6275,8198}, {6287,8200}, {8190,9918}, {10064,11877}, {10080,11879}, {11366,12264}, {11384,12144}, {11492,12339}, {11822,12122}, {11837,12206}, {11843,12252}
X(12476) = reflection of X(12477) in X(55)
X(12476) = X(83)-of-1st-Auriga-triangle
X(12476) = X(7977)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12477) lies on these lines: {55,12476}, {83,5598}, {732,12453}, {754,11208}, {2896,5602}, {5597,7977}, {5600,6292}, {6249,8203}, {6274,8206}, {6275,8205}, {6287,8207}, {8187,9903}, {8191,9918}, {10064,11878}, {10080,11880}, {11367,12264}, {11385,12144}, {11493,12339}, {11823,12122}, {11838,12206}, {11844,12252}
X(12477) = reflection of X(12476) in X(55)
X(12477) = X(83)-of-2nd-Auriga-triangle
X(12477) = X(7977)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12478) lies on these lines: {55,12479}, {112,11822}, {127,8196}, {2799,12179}, {2806,12462}, {3320,11873}, {5601,12384}, {9517,12365}, {9530,11207}, {11366,12265}, {11492,12340}, {11837,12207}
X(12478) = reflection of X(12479) in X(55)
X(12478) = X(1297)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12479) lies on these lines: {55,12478}, {112,11823}, {127,8203}, {2799,12180}, {2806,12463}, {3320,11874}, {5602,12384}, {8187,12408}, {9517,12366}, {9530,11208}, {11367,12265}, {11493,12340}, {11838,12207}
X(12479) = reflection of X(12478) in X(55)
X(12479) = X(1297)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12480) lies on these lines: {54,5597}, {55,12481}, {195,11875}, {539,11207}, {1154,11252}, {1209,5599}, {2888,5601}, {3574,8196}, {5598,7979}, {7691,11822}, {10066,11877}, {10082,11879}, {10628,12365}, {11366,12266}, {11492,12341}, {11837,12208}, {11843,12254}
X(12480) = reflection of X(12481) in X(55)
X(12480) = X(54)-of-1st-Auriga-triangle
X(12480) = X(7979)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12481) lies on these lines: {54,5598}, {55,12480}, {195,11876}, {539,11208}, {1154,11253}, {1209,5600}, {2888,5602}, {3574,8203}, {5597,7979}, {7691,11823}, {8187,9905}, {10066,11878}, {10082,11880}, {10628,12366}, {11367,12266}, {11493,12341}, {11838,12208}, {11844,12254}
X(12481) = reflection of X(12480) in X(55)
X(12481) = X(54)-of-2nd-Auriga-triangle
X(12481) = X(7979)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12482) lies on these lines: {55,12483}, {5597,10266}, {8190,12414}, {11366,12267}, {11492,12342}, {11837,12209}, {11843,12255}
X(12482) = reflection of X(12483) in X(55)
X(12482) = X(10266)-of-1st-Auriga-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12483) lies on these lines: {55,12482}, {5598,10266}, {8187,12409}, {8191,12414}, {11367,12267}, {11493,12342}, {11838,12209}, {11844,12255}
X(12483) = reflection of X(12482) in X(55)
X(12483) = X(10266)-of-2nd-Auriga-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12484) lies on these lines: {55,12485}, {486,5597}, {487,5601}, {642,5599}, {3564,12415}, {5598,7980}, {6251,8196}, {6280,8199}, {6281,8198}, {6290,8200}, {9986,11861}, {10067,11877}, {10083,11879}, {11366,12268}, {11492,12343}, {11822,12123}, {11837,12210}, {11843,12256}
X(12484) = reflection of X(12485) in X(55)
X(12484) = X(486)-of-inner-Vecten-triangle
X(12484) = X(7980)-of-outer-Vecten-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12485) lies on these lines: {55,12484}, {486,5598}, {487,5602}, {642,5600}, {3564,12416}, {5597,7980}, {6251,8203}, {6280,8206}, {6281,8205}, {6290,8207}, {8187,9906}, {9986,11862}, {10067,11878}, {10083,11880}, {11367,12268}, {11493,12343}, {11823,12123}, {11838,12210}, {11844,12256}
X(12485) = reflection of X(12484) in X(55)
X(12485) = X(486)-of-outer-Vecten-triangle
X(12485) = X(7980)-of-inner-Vecten-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12486) lies on these lines: {55,12487}, {485,5597}, {488,5601}, {641,5599}, {3564,12415}, {5598,7981}, {6250,8196}, {6278,8199}, {6279,8198}, {6289,8200}, {9987,11861}, {10068,11877}, {10084,11879}, {11366,12269}, {11492,12344}, {11822,12124}, {11837,12211}, {11843,12257}
X(12486) = reflection of X(12487) in X(55)
X(12486) = X(485)-of-inner-Vecten-triangle
X(12486) = X(7981)-of-outer-Vecten-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12487) lies on these lines: {55,12486}, {485,5598}, {488,5602}, {641,5600}, {3564,12416}, {5597,7981}, {6250,8203}, {6278,8206}, {6279,8205}, {6289,8207}, {8187,9907}, {9987,11862}, {10068,11878}, {10084,11880}, {11367,12269}, {11493,12344}, {11823,12124}, {11838,12211}, {11844,12257}
X(12487) = reflection of X(12486) in X(55)
X(12487) = X(485)-of-outer-Vecten-triangle
X(12487) = X(7981)-of-inner-Vecten-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12488) lies on these lines: {3,363}, {4,9783}, {40,8140}, {72,11685}, {517,9805}, {942,8113}, {1071,11886}, {1385,8109}, {1482,11527}, {3579,8107}, {5045,11026}, {5728,8385}, {5777,5934}, {6732,8100}, {8099,8133}, {8377,9955}, {8380,9956}, {8390,9957}, {8391,9959}, {9940,11854}, {9947,11856}, {10441,11892}
X(12488) = midpoint of X(9805) and X(9836)
X(12488) = reflection of X(12489) in X(40)
X(12488) = X(5)-of-inner-Hutson-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12489) lies on these lines: {3,168}, {4,9787}, {40,8140}, {72,11686}, {178,946}, {517,9806}, {942,8114}, {1071,11887}, {1385,8110}, {1482,11528}, {3579,8108}, {5045,11027}, {5728,8386}, {5777,5935}, {8099,8135}, {8100,8138}, {8378,9955}, {8381,9956}, {8392,9957}, {9940,11855}, {9947,11857}, {9959,11926}, {10441,11893}
X(12489) = midpoint of X(9806) and X(9837)
X(12489) = reflection of X(12488) in X(40)
X(12489) = X(5)-of-outer-Hutson-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12490) lies on these lines: {3,8231}, {4,9789}, {5,3739}, {40,8244}, {72,11687}, {517,7596}, {942,8243}, {1335,7133}, {1385,8225}, {1482,11532}, {3579,8224}, {5045,11030}, {5728,8237}, {5777,8233}, {8099,8247}, {8100,8248}, {8228,9955}, {8230,9956}, {8239,9957}, {8246,9959}, {9940,10858}, {9947,10867}, {10441,10891}
X(12490) = midpoint of X(7596) and X(9808)
X(12490) = X(5)-of-2nd-Pamfilos-Zhou-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12491) lies on these lines: {1,10502}, {4,11891}, {40,8423}, {72,8126}, {174,942}, {258,5708}, {517,8130}, {1159,11899}, {1385,7587}, {1482,11535}, {5045,8083}, {5439,8125}, {5728,8389}, {8129,8729}, {8382,9956}, {8425,9959}, {9947,11860}, {9957,11924}, {10441,11896}, {11996,12490}
X(12491) = midpoint of X(8351) and X(12445)
X(12491) = X(5)-of-Yff-central-triangle
X(12491) = {X(11195), X(12445)}-harmonic conjugate of X(8351)
The reciprocal orthologic center of these triangles is X(1).
X(12492) lies on these lines: {1,483}, {177,481}, {8083,8093}
X(12492) = reflection of X(12493) in X(1)
X(12492) = X(485)-of-mid-arc-triangle
X(12492) = X(12124)-of-2nd-mid-arc-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12493) lies on these lines: {1,483}, {8094,10968}
X(12493) = reflection of X(12492) in X(1)
X(12493) = X(485)-of-2nd-mid-arc-triangle
X(12493) = X(12124)-of-mid-arc-triangle
The reciprocal orthologic center of these triangles is X(6232).
X(12494) lies on the nine-points circle and these lines: {2,6233}, {4,6323}, {114,9771}, {543,11569}
X(12494) = midpoint of X(4) and X(6323)
X(12494) = complement of X(6233)
X(12494) = reflection of X(13234) in X(5)
X(12494) = 2nd-Brocard-to-5th-Euler similarity image of X(6232)
The reciprocal orthologic center of these triangles is X(10).
X(12495) lies on these lines: {1,3096}, {8,32}, {10,7846}, {145,2896}, {355,9993}, {517,9873}, {519,7811}, {944,3098}, {952,9821}, {1482,9996}, {2098,10874}, {2099,10873}, {3094,5846}, {3099,3632}, {3241,7865}, {3616,7914}, {3617,10583}, {3913,11494}, {5603,10356}, {7967,10357}, {9862,12245}, {10047,10573}, {10345,10800}, {10348,12194}, {10828,12410}, {10871,10912}, {10877,10950}, {11386,12135}, {11861,12454}, {11862,12455}
X(12495) = orthologic center of these triangles: 5th Brocard to 2nd Schiffler
a
X(12495) = X(8)-of-5th-Brocard-triangle
X(12495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9857,3096), (10,11368,7846), (145,2896,9997)
The reciprocal orthologic center of these triangles is X(40).
X(12496) lies on these lines: {32,84}, {515,12495}, {971,9821}, {1490,3098}, {1709,10038}, {3096,6260}, {3099,7992}, {5658,10357}, {6001,9941}, {6245,9993}, {6257,9995}, {6258,9994}, {6259,9996}, {6705,7846}, {7971,9997}, {9862,12246}, {9910,10828}, {10047,10085}, {11368,12114}, {11386,12136}, {11494,12330}, {11861,12456}, {11862,12457}
X(12496) = X(84)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12497) lies on these lines: {1,3098}, {3,11368}, {4,9857}, {10,9993}, {32,40}, {46,10047}, {65,10877}, {484,7132}, {515,12495}, {516,9873}, {517,9821}, {946,3096}, {962,2896}, {1699,10356}, {1836,10873}, {1902,11386}, {3099,7991}, {5119,10038}, {5184,9301}, {5603,10357}, {5812,10872}, {6361,9862}, {6684,7846}, {7914,8227}, {7982,9997}, {9911,10828}, {10306,11494}, {11861,12458}, {11862,12459}
X(12497) = reflection of X(9941) in X(9821)
X(12497) = X(40)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12498) lies on these lines: {11,11368}, {32,80}, {100,9857}, {214,3096}, {952,9941}, {2800,9873}, {2802,12495}, {2829,12496}, {2896,6224}, {3098,12119}, {3099,9897}, {5840,12497}, {6262,9995}, {6263,9994}, {6265,9996}, {6702,7846}, {7972,9997}, {9862,12247}, {9912,10828}, {10038,10057}, {10047,10073}, {11386,12137}, {11494,12331}, {11861,12460}, {11862,12461}
X(12498) = X(80)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12499) lies on these lines: {11,9993}, {32,104}, {100,3098}, {119,3096}, {153,2896}, {214,3061}, {515,12498}, {952,9821}, {1317,10877}, {1768,3099}, {2783,8782}, {2787,9862}, {2800,9941}, {2802,12497}, {2829,9873}, {6713,7846}, {7865,10711}, {9913,10828}, {9978,9999}, {9980,9998}, {9996,10742}, {9997,10698}, {10038,10058}, {10047,10074}, {11368,11715}, {11386,12138}, {11494,12332}, {11861,12462}, {11862,12463}
X(12499) = X(104)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12500) lies on these lines: {32,7160}, {2896,9874}, {3098,12120}, {3099,9898}, {8000,9997}, {9862,12249}, {10038,10059}, {10047,10075}, {10828,12411}, {11368,12260}, {11386,12139}, {11494,12333}, {11861,12464}, {11862,12465}
X(12500) = X(7160)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12501) lies on these lines: {32,265}, {67,3098}, {110,9996}, {542,1569}, {1511,3096}, {2771,12498}, {2896,12383}, {3099,12407}, {3448,9862}, {5663,9873}, {9993,10113}, {10088,10873}, {10091,10874}, {10828,12412}, {11368,12261}, {11386,12140}, {11494,12334}, {11861,12466}, {11862,12467}
X(12501) = X(265)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12502) lies on these lines: {30,9923}, {32,64}, {1498,3098}, {2777,12501}, {2883,3096}, {2896,6225}, {3099,9899}, {5656,10357}, {5878,9996}, {6000,9821}, {6001,12497}, {6247,9993}, {6266,9995}, {6267,9994}, {6696,7846}, {7355,10877}, {7973,9997}, {9862,12250}, {9914,10828}, {10038,10060}, {10047,10076}, {11368,12262}, {11381,11386}, {11494,12335}, {11861,12468}, {11862,12469}
X(12502) = X(64)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12503) lies on these lines: {32,1297}, {112,3098}, {127,9993}, {132,3096}, {2794,8782}, {2799,9862}, {2806,12499}, {2896,12384}, {3099,12408}, {3320,10877}, {7811,9530}, {9157,9999}, {9517,9984}, {10828,12413}, {11368,12265}, {11386,12145}, {11494,12340}, {11861,12478}, {11862,12479}
X(12503) = X(1297)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12504) lies on these lines: {32,10266}, {3099,12409}, {9862,12255}, {10828,12414}, {11368,12267}, {11386,12146}, {11494,12342}, {11861,12482}, {11862,12483}
X(12504) = X(10266)-of-5th-Brocard-triangle
The reciprocal orthologic center of these triangles is X(12506).
X(12505) lies on these lines: {3,9829}, {4,3849}, {5,5913}, {20,6031}, {631,10163}, {3090,10162}, {5067,10173}, {6232,7770}
X(12505) = X(4)-of-circummedial-triangle
The reciprocal orthologic center of these triangles is X(12505).
X(12506) lies on these lines: {2,12505}, {3,3849}, {4,6032}, {5,9172}, {140,10163}, {631,9829}, {1656,10173}, {3523,6031}
X(12506) = complement of X(12505)
X(12506) = orthoptic-circle-of-Steiner-inellipse-inverse of X(39157)
The reciprocal orthologic center of these triangles is X(12508).
X(12507) lies on the circumcircle and these lines: {2697,8705}, {2781,6325}, {6236,9517}
The reciprocal orthologic center of these triangles is X(12507).
X(12508) lies on the line {1316,6232}
X(12508) = X(12507)-of-1st-orthosymmedial-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12509) lies on these lines: {3,12169}, {4,487}, {20,3564}, {25,12311}, {54,12229}, {69,9991}, {376,5860}, {378,12303}, {486,631}, {637,6337}, {642,3090}, {3533,6119}, {3545,6251}, {3567,12237}, {5657,9906}, {5889,12274}, {5890,12285}, {7582,12210}, {7612,10851}, {9738,12322}, {9921,12088}, {10625,12223}
X(12509) = midpoint of X(5889) and X(12274)
X(12509) = reflection of X(i) in X(j) for these (i,j): (4,487), (12221,3), (12256,12123), (12296,6290)
X(12509) = orthic-to-circumorthic similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12510) lies on these lines: {3,12170}, {4,488}, {20,3564}, {25,12312}, {54,12230}, {69,9992}, {376,5861}, {378,12304}, {485,631}, {638,6337}, {641,3090}, {3533,6118}, {3545,6250}, {3567,12238}, {5210,9540}, {5657,9907}, {5889,12275}, {5890,12286}, {7581,12211}, {7612,10852}, {9739,12323}, {9922,12088}, {10625,12224}
X(12510) = midpoint of X(5889) and X(12275)
X(12510) = reflection of X(i) in X(j) for these (i,j): (4,488), (12222,3), (12257,12124), (12297,6289)
X(12510) = orthic-to-circumorthic similarity image of X(488)
The reciprocal orthologic center of these triangles is X(1).
X(12511) lies on these lines: {1,7411}, {3,142}, {4,3841}, {10,5584}, {20,993}, {35,4295}, {36,3522}, {40,758}, {55,3671}, {56,4314}, {58,1742}, {72,7964}, {100,3984}, {165,411}, {191,9961}, {376,11012}, {386,9441}, {404,4512}, {550,5450}, {551,8273}, {1490,3678}, {1621,9589}, {1699,6986}, {1709,3647}, {1754,4300}, {2077,6876}, {3146,5251}, {3149,10164}, {3357,3579}, {3361,4326}, {3428,4297}, {3528,10596}, {3587,6261}, {3635,8158}, {3814,6838}, {3822,6908}, {3825,6865}, {3874,10884}, {3916,5918}, {4229,4278}, {5259,9812}, {5715,6701}, {6361,10902}, {6681,6926}, {6684,6985}, {6763,11220}, {7742,10624}, {10393,12432}, {10860,12446}
X(12511) = midpoint of X(3671) and X(5493)
X(12511) = reflection of X(i) in X(j) for these (i,j): (4,3841), (5248,3)
X(12511) = X(578)-of-1st-circumperp-triangle
X(12511) = complement, wrt 1st circumperp triangle, of X(12514)
X(12511) = complement, wrt excentral triangle, of X(12514)
X(12511) = excentral-to-1st-circumperp similarity image of X(12514)
X(12511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3428,4297,8666), (5584,7580,10)
The reciprocal orthologic center of these triangles is X(1).
As a point P moves on the circumcircle, the centroid of the 12 excenters of triangles ABC, BCP, CAP, ABP traces a curvilinear triangle, T. Let A', B', C' be the vertices of T, and (Oa), (Ob), (Oc) the circles whose arcs form the sides of T; the triangle A'B'C' is also the orthic triangle of the anticomplementary triangle of OaObOc, and OaObOc the medial triangle of the excentral triangle of A'B'C'. Then A'B'C' is homothetic to the medial triangle at X(12512). Let A" be the intersection, other than A', of circles (Ob) and (Oc), and define B" and C" cyclically. Then A"B"C" is the excentral triangle of A'B'C', and the anticomplementary triangle of OaObOc. Also, A"B"C" is homothetic to the extraversion triangle of X(10) (i.e. the complement of the excentral triangle) at X(12512). (Randy Hutson, July 21, 2017)
X(12512) lies on these lines: {1,3522}, {2,10248}, {3,142}, {4,3634}, {10,20}, {30,3828}, {35,4292}, {36,10624}, {40,376}, {46,4304}, {55,4298}, {57,4314}, {58,4229}, {63,6743}, {72,5918}, {140,10171}, {226,5217}, {355,3534}, {382,10175}, {386,1742}, {390,3361}, {411,6700}, {498,4333}, {515,550}, {517,548}, {546,10172}, {551,962}, {631,3817}, {726,5188}, {758,9943}, {936,2951}, {942,10178}, {950,1155}, {960,9858}, {971,3678}, {975,1721}, {993,5584}, {1040,4347}, {1158,3587}, {1210,4302}, {1385,8703}, {1420,4342}, {1587,9582}, {1697,4315}, {1698,3146}, {1699,3523}, {1703,9541}, {1737,4324}, {1770,5010}, {2077,3651}, {2093,4305}, {3244,5731}, {3339,4313}, {3474,3601}, {3486,5128}, {3524,8227}, {3528,3576}, {3529,5587}, {3530,9955}, {3543,7989}, {3616,9589}, {3624,9812}, {3627,11231}, {3755,4252}, {3811,5732}, {3833,5806}, {3841,8727}, {3874,7957}, {3911,6284}, {3916,7964}, {3947,5218}, {3956,9947}, {4192,6686}, {4294,11019}, {4308,9819}, {4311,5119}, {4312,5703}, {4316,10039}, {4330,5131}, {4353,5266}, {4355,10578}, {4512,6904}, {4652,4847}, {4691,5657}, {4701,11362}, {4746,5881}, {5059,9780}, {5204,12053}, {5267,6909}, {5281,5290}, {5438,5698}, {5692,9961}, {5818,11001}, {5842,6705}, {5904,11220}, {6244,8715}, {6409,8983}, {6460,9616}, {6872,8582}, {6906,7688}, {6987,10270}, {7288,9580}, {7988,10303}, {9899,11206}, {9949,10860}, {10391,12432}
X(12512) = midpoint of X(i) and X(j) for these {i,j}: {1,5493}, {10,20}, {40,4297}, {550,3579}, {3244,7991}, {3874,7957}, {4301,6361}
X(12512) = reflection of X(i) in X(j) for these (i,j): (4,3634), (1125,3), (4301,3636), (4701,11362), (5881,4746), (9955,3530)
X(12512) = X(389)-of-1st-circumperp-triangle
X(12512) = X(10110)-of-hexyl-triangle
X(12512) = X(11793)-of-excentral-triangle
X(12512) = excentral-to-1st-circumperp similarity image of X(10)
X(12512) = excentral-to-2nd-Conway similarity image of X(12571)
X(12512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,9778,5493), (3,11495,12511), (4,10164,3634), (20,165,10), (40,376,4297), (46,4304,6738), (57,4314,6744), (962,7987,551), (962,10304,7987), (3474,3601,3671), (3522,9778,1), (3528,6361,3576), (3576,4301,3636), (3576,6361,4301), (5218,9579,3947), (5248,12436,1125), (5731,7991,3244), (7957,10167,3874)
The reciprocal orthologic center of these triangles is X(1).
X(12513) lies on these lines: {1,6}, {2,3304}, {3,519}, {4,529}, {5,11236}, {8,56}, {10,999}, {11,3436}, {12,6933}, {20,528}, {21,3241}, {35,3633}, {36,3632}, {40,3880}, {46,10914}, {55,145}, {57,4853}, {63,3057}, {75,7176}, {78,1319}, {100,3621}, {104,5854}, {105,6553}, {106,8688}, {144,8163}, {165,2136}, {198,5839}, {200,1420}, {241,6167}, {312,9369}, {355,10680}, {377,5434}, {382,535}, {388,2886}, {391,1696}, {443,9710}, {474,3679}, {480,6049}, {516,8158}, {517,1158}, {524,9840}, {527,4301}, {604,3713}, {672,4513}, {758,1482}, {908,11376}, {936,4662}, {940,10459}, {944,3428}, {952,11249}, {961,1219}, {988,4646}, {993,3244}, {1005,3486}, {1012,7982}, {1043,3286}, {1125,7373}, {1145,10074}, {1155,3893}, {1201,4383}, {1259,1317}, {1329,3086}, {1385,3811}, {1388,4511}, {1398,1861}, {1407,9363}, {1457,9370}, {1468,5710}, {1475,4390}, {1483,5428}, {1610,8301}, {1617,6737}, {1621,3623}, {1697,4640}, {1706,3361}, {1727,5697}, {1776,2098}, {1818,4322}, {2099,3868}, {2319,11051}, {2321,5120}, {2475,9657}, {2476,11237}, {2478,11240}, {2550,3600}, {2551,3816}, {2646,3870}, {2802,11256}, {3035,7080}, {3058,6872}, {3085,4999}, {3091,3829}, {3149,5881}, {3158,7987}, {3189,5584}, {3207,3684}, {3219,3890}, {3306,3698}, {3333,3812}, {3338,3753}, {3339,10107}, {3434,7354}, {3475,11281}, {3501,5022}, {3509,4051}, {3576,6765}, {3616,8167}, {3617,4413}, {3622,4423}, {3626,9709}, {3635,5248}, {3680,3928}, {3689,4855}, {3740,8583}, {3741,5793}, {3754,5708}, {3820,10200}, {3838,5290}, {3871,5217}, {3878,3927}, {3895,4652}, {3901,11009}, {3911,6736}, {3916,5119}, {3962,5048}, {4187,10072}, {4252,5255}, {4293,5082}, {4297,5853}, {4298,5880}, {4313,9797}, {4317,11112}, {4361,6647}, {4673,5695}, {4847,5794}, {4882,5438}, {4921,7419}, {4930,7489}, {5046,11238}, {5080,10896}, {5130,11401}, {5231,9578}, {5250,5919}, {5252,6734}, {5298,6921}, {5432,10528}, {5433,5552}, {5450,10306}, {5690,10269}, {5698,9785}, {5732,9845}, {5734,6912}, {5784,9850}, {5795,11019}, {5844,11248}, {5886,12001}, {6668,8164}, {6910,11239}, {7483,10056}, {7966,10268}, {8240,8424}, {9053,12329}, {9670,11114}, {9671,10707}, {10475,11679}, {10522,10949}, {10526,10943}, {10530,10955}, {10860,12448}, {10895,11680}, {10950,10966}, {10953,10959}, {11492,12455}, {11493,12454}, {11827,12116}
X(12513) = midpoint of X(i) and X(j) for these {i,j}: {1,6762}, {2136,11519}, {3189,6764}, {3680,7991}
X(12513) = reflection of X(i) in X(j) for these (i,j): (1,11260), (3,8666), (4,3813), (355,10916), (3811,1385), (3913,3), (4421,11194), (10306,5450), (10526,10943), (11500,11249)
X(12513) = orthologic center of these triangles: 1st circumperp to 2nd Schiffler
X(12513) = X(64)-of-1st-circumperp-triangle
X(12513) = X(1498)-of-2nd-circumperp-triangle
X(12513) = X(2883)-of-excentral-triangle
X(12513) = X(6247)-of-hexyl-triangle
X(12513) = excentral-to-1st-circumperp similarity image of X(2136)
X(12513) = excentral-to-2nd-circumperp similarity image of X(6762)
X(12513) = excentral-to-hexyl similarity image of X(3913)
X(12513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,72,5289), (1,238,1616), (1,956,958), (1,958,1001), (1,5247,1191), (1,5258,405), (1,5288,956), (1,5904,5730), (3,3913,4421), (3,8666,11194), (4,3813,11235), (8,56,1376), (8,1788,8256), (21,3241,3303), (21,3303,4428), (405,956,5258), (405,5258,958), (1476,5435,56), (3436,10529,11), (3913,11194,3)
The reciprocal orthologic center of these triangles is X(65).
X(12514) lies on these lines: {1,21}, {2,46}, {3,960}, {4,9}, {6,3931}, {8,90}, {20,1709}, {29,1748}, {30,5794}, {35,78}, {36,4652}, {37,5711}, {44,4646}, {55,72}, {56,392}, {57,1125}, {65,405}, {84,4297}, {92,3559}, {100,3876}, {109,1038}, {165,411}, {171,975}, {190,4385}, {200,1005}, {201,1395}, {210,1898}, {214,1768}, {221,1214}, {226,10198}, {238,986}, {329,3085}, {355,5842}, {377,1770}, {386,1245}, {387,1723}, {406,1452}, {442,1836}, {443,3474}, {452,1728}, {474,1155}, {484,1698}, {495,5857}, {497,10916}, {498,908}, {515,5837}, {517,958}, {518,3295}, {519,1697}, {535,9613}, {551,3333}, {560,6042}, {612,5264}, {614,3670}, {902,976}, {912,10267}, {940,6051}, {942,1001}, {946,5709}, {956,3057}, {962,5273}, {984,5255}, {988,995}, {1107,1572}, {1150,3702}, {1156,4606}, {1193,4414}, {1203,5256}, {1329,6842}, {1334,5282}, {1376,3579}, {1385,5289}, {1445,3339}, {1454,7483}, {1479,6734}, {1490,10268}, {1571,1575}, {1610,4221}, {1656,5087}, {1699,5705}, {1714,3914}, {1724,4424}, {1727,3612}, {1737,2478}, {1741,5706}, {1743,4868}, {1759,2198}, {1760,5263}, {1761,5327}, {1782,10319}, {1788,5084}, {1837,7082}, {2093,3754}, {2136,3625}, {2245,4205}, {2257,4356}, {2646,5730}, {2802,4853}, {2886,5791}, {2950,10270}, {2951,5785}, {3052,5266}, {3086,5744}, {3158,4134}, {3218,3338}, {3244,6762}, {3303,3555}, {3306,3336}, {3358,9948}, {3359,3452}, {3361,4973}, {3416,3695}, {3419,6284}, {3421,10915}, {3436,10039}, {3550,5293}, {3576,5267}, {3587,6869}, {3632,3895}, {3634,5128}, {3646,5437}, {3650,10404}, {3654,8256}, {3679,5086}, {3681,3871}, {3682,4300}, {3685,10449}, {3689,4005}, {3697,3715}, {3698,5183}, {3704,5814}, {3711,4533}, {3714,5774}, {3740,9709}, {3742,5708}, {3746,3870}, {3812,8257}, {3817,6855}, {3822,9612}, {3831,4011}, {3911,10200}, {3913,5220}, {4008,11683}, {4067,11523}, {4084,5436}, {4187,4679}, {4197,4338}, {4199,10974}, {4304,6737}, {4307,5279}, {4326,5223}, {4423,5221}, {4426,9620}, {4450,5300}, {4647,5271}, {4666,4880}, {4668,5541}, {4847,10624}, {4855,5010}, {4999,5886}, {5046,10826}, {5080,10827}, {5217,5440}, {5227,5847}, {5231,9614}, {5234,6912}, {5247,7262}, {5259,5902}, {5290,8545}, {5295,5695}, {5302,5836}, {5438,6876}, {5506,10129}, {5535,6852}, {5536,11522}, {5693,10902}, {5720,6796}, {5731,10085}, {5732,7992}, {5743,5955}, {5755,5799}, {5777,11500}, {5795,6930}, {5812,7680}, {5815,6172}, {5880,8728}, {6690,11374}, {6700,6988}, {6867,10175}, {6870,9812}, {6871,9780}, {6913,7686}, {6932,9588}, {7085,8193}, {7162,10528}, {7373,10179}, {7411,9961}, {7548,7989}, {7969,9678}, {8273,10167}, {8424,9959}, {8580,12446}, {9589,10883}, {9778,9800}, {9949,10860}, {9957,12513}, {11344,11507}
X(12514) = midpoint of X(i) and X(j) for these {i,j}: {8,4294}, {3295,3927}, {4326,5223}
X(12514) = reflection of X(i) in X(j) for these (i,j): (1,5248), (3671,1125)
X(12514) = complement of X(4295)
X(12514) = X(578)-of-excentral-triangle
X(12514) = complement, wrt excentral triangle, of X(12565)
X(12514) = anticomplement, wrt 1st circumperp triangle, of X(12511)
X(12514) = anticomplement, wrt excentral triangle, of X(12511)
X(12514) = 1st-circumperp-to-excentral similarity image of X(12511)
X(12514) = 2nd-circumperp-to-excentral similarity image of X(5248)
X(12514) = intouch-to-excentral similarity image of X(3671)
X(12514) = inner-Conway-to-excentral similarity image of X(12526)
X(12514) = orthologic center of these triangles: excentral to 4th Conway
X(12514) = Ursa-major-to-excentral similarity image of X(17646)
X(12514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,191,63), (1,1707,58), (1,3899,11682), (1,3901,11520), (1,4512,5248), (2,11415,12047), (3,960,997), (3,5887,6261), (9,3496,169), (21,3869,1), (31,2292,1), (38,3915,1), (63,5250,1), (71,2354,573), (960,4640,3), (993,3878,1), (1621,3868,1), (1621,11684,3868), (2975,3877,1), (3647,3878,993), (3884,8666,1), (6212,6213,573)
The reciprocal orthologic center of these triangles is X(3869).
X(12515) lies on these lines: {3,214}, {8,12248}, {9,119}, {10,3652}, {11,46}, {20,12247}, {30,80}, {35,11571}, {40,550}, {55,11570}, {57,1387}, {63,1145}, {65,10058}, {72,74}, {104,517}, {149,6361}, {153,5657}, {165,6326}, {191,11698}, {355,1158}, {376,6224}, {381,6702}, {516,10265}, {912,3689}, {1155,10090}, {1317,3655}, {1385,10698}, {1482,4757}, {1484,5535}, {1537,3306}, {1728,5128}, {1782,2828}, {1836,8068}, {2077,4867}, {2320,6950}, {2801,11495}, {2802,11256}, {3035,12514}, {3057,10074}, {3219,10711}, {3295,5083}, {3587,9945}, {5884,11849}, {6001,6100}, {6264,7991}, {6284,10073}, {6797,7098}, {6905,10225}, {7354,10057}, {7411,9964}, {7972,11010}, {9778,9803}, {9952,10860}
X(12515) = midpoint of X(i) and X(j) for these {i,j}: {8,12248}, {20,12247}, {40,1768}, {149,6361}, {6264,7991}
X(12515) = reflection of X(i) in X(j) for these (i,j): (100,3579), (1482,11715), (1537,6713), (6265,3), (6905,10225), (10698,1385), (10738,10265), (10742,10), (12119,550)
X(12515) = X(265)-of-1st-circumperp-triangle
X(12515) = X(12121)-of-2nd-circumperp-triangle
X(12515) = X(1511)-of-excentral-triangle
X(12515) = X(10113)-of-hexyl-triangle
X(12515) = X(1387)-of-tangential-of-excentral-triangle
X(12515) = excentral-to-1st-circumperp similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3555).
X(12516) lies on these lines: {3,12333}, {9,946}, {40,6764}, {56,5920}, {165,8001}, {1158,5493}, {3333,3523}, {3361,9898}, {3651,12120}, {5045,12260}, {9778,9804}, {9953,10860}
X(12516) = reflection of X(12521) in X(3)
The reciprocal orthologic center of these triangles is X(3555).
X(12517) lies on these lines: {3,12442}, {19,1598}, {522,8668}, {946,6911}, {10860,12449}
X(12517) = reflection of X(12522) in X(3)
The reciprocal orthologic center of these triangles is X(1).
X(12518) lies on these lines: {3,12443}, {55,177}, {56,8422}, {57,5571}, {100,11691}, {164,165}, {7670,7676}, {9778,9807}, {10860,12450}
X(12518) = midpoint of X(164) and X(167)
X(12518) = orthologic center of these triangles: 1st circumperp to 2nd midarc
X(12518) = reflection of X(12523) in X(3)
X(12518) = X(1)-of-1st-circumperp-triangle
X(12518) = X(40)-of-2nd-circumperp-triangle
X(12518) = X(10)-of-excentral-triangle
X(12518) = X(946)-of-hexyl-triangle
X(12518) = {X(165), X(167)}-harmonic conjugate of X(164)
The reciprocal orthologic center of these triangles is X(21).
X(12519) lies on these lines: {3,12342}, {2475,3925}, {10860,12451}
X(12519) = reflection of X(12524) in X(3)
The reciprocal orthologic center of these triangles is X(65).
X(12520) lies on these lines: {1,7}, {3,960}, {10,1490}, {21,1709}, {40,758}, {46,411}, {56,10167}, {65,7580}, {72,480}, {78,165}, {84,993}, {103,1310}, {224,3869}, {355,9710}, {392,8273}, {515,6850}, {572,1973}, {936,10164}, {946,6851}, {958,971}, {1001,9856}, {1040,10571}, {1125,6847}, {1214,1854}, {1319,10866}, {1385,11496}, {1467,11019}, {1699,6895}, {1708,1858}, {1737,6838}, {1750,5177}, {1768,4652}, {2475,5691}, {2551,5658}, {2646,5918}, {2886,5787}, {2975,10085}, {3243,6766}, {3359,6796}, {3522,4511}, {3576,5248}, {3601,10860}, {3612,6909}, {3616,9800}, {3624,6888}, {3841,5587}, {3870,7991}, {3878,7971}, {3962,7964}, {4189,4512}, {4666,11522}, {5302,5779}, {5436,11372}, {5450,7171}, {5493,6769}, {5534,11362}, {5693,7688}, {5709,5884}, {5715,11263}, {5720,6684}, {5745,9948}, {5768,10916}, {6282,12512}, {6836,12047}, {6845,8227}, {6892,10165}, {6925,10572}, {6932,10826}, {8583,9949}, {10864,12446}
X(12520) = midpoint of X(20) and X(4295)
X(12520) = reflection of X(i) in X(j) for these (i,j): (40,12511), (11496,1385), (12514,3)
X(12520) = complement, wrt hexyl triangle, of X(12705)
X(12520) = anticomplement, wrt 2nd circumperp triangle, of X(5248)
X(12520) = excentral-to-2nd-circumperp similarity image of X(12565)
X(12520) = excentral-to-1st-circumperp similarity image of X(12526)
X(12520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1044,1448), (1,5732,4297), (3,6261,997), (21,9961,1709), (2975,11220,10085)
The reciprocal orthologic center of these triangles is X(3555).
X(12521) lies on these lines: {3,12333}, {21,3870}, {55,5920}, {100,3333}, {224,11036}, {1001,3811}, {3528,12120}, {3616,9804}, {3913,5045}, {3957,9874}, {4301,6261}, {5732,6769}, {7987,8001}, {8583,9953}, {10385,10393}
X(12521) = reflection of X(12516) in X(3)
The reciprocal orthologic center of these triangles is X(3555).
X(12522) lies on these lines: {3,12442}, {8583,12449}
X(12522) = reflection of X(12517) in X(3)
The reciprocal orthologic center of the 2nd circumperp and midarc triangles is X(1).
X(12523) lies on the cubics K838 and K1271 and these lines: {1, 164}, {2, 12622}, {3, 12443}, {4, 12614}, {21, 12539}, {55, 8422}, {56, 177}, {57, 31768}, {167, 7987}, {188, 3659}, {260, 8241}, {363, 10233}, {388, 31734}, {405, 12694}, {497, 31769}, {503, 21214}, {504, 7707}, {958, 18258}, {999, 12908}, {1125, 21633}, {1385, 53810}, {1697, 31767}, {2646, 17641}, {2975, 11691}, {3295, 32183}, {3303, 11234}, {3304, 11191}, {3576, 12844}, {3616, 9807}, {4293, 31735}, {4294, 31770}, {5666, 52999}, {6244, 31800}, {7587, 13092}, {7670, 7677}, {7991, 8108}, {8091, 10496}, {8109, 12879}, {8110, 12884}, {8225, 13090}, {8583, 12450}, {10215, 42614}, {10882, 12554}, {12513, 47303}, {17614, 17657}
X(12523) = midpoint of X(i) and X(j) for these {i,j}: {1, 164}, {7991, 11528}, {12656, 55169}, {55168, 55175}, {55170, 55173}, {55171, 55172}
X(12523) = reflection of X(i) in X(j) for these {i,j}: {1, 55172}, {4, 12614}, {164, 55171}, {12518, 3}, {21633, 1125}, {55170, 164}, {55173, 1}, {55176, 55175}
X(12523) = anticomplement of X(12622)
X(12523) = orthologic center of these triangles: 2nd circumperp to 2nd midarc
X(12523) = X(1)-of-2nd-circumperp-triangle
X(12523) = X(40)-of-1st-circumperp-triangle
X(12523) = X(10)-of-hexyl-triangle
X(12523) = X(946)-of-excentral-triangle
X(12523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 55168, 164}, {1, 55169, 12656}, {1, 55171, 55170}, {1, 55172, 55176}, {1, 55175, 55172}, {164, 12656, 55169}, {164, 55168, 55171}, {164, 55172, 55173}, {164, 55175, 1}, {7588, 8077, 1}, {55168, 55172, 55170}, {55170, 55176, 55173}, {55171, 55175, 55173}, {55173, 55176, 1}
The reciprocal orthologic center of these triangles is X(21).
X(12524) lies on these lines: {1,6597}, {3,12342}, {12,100}, {21,10266}, {1001,12267}, {5443,6599}, {8583,12451}
X(12524) = reflection of X(12519) in X(3)
The reciprocal orthologic center of these triangles is X(99).
X(12525) lies on the McCay circumcircle and these lines: {2,9879}, {3,5106}, {183,6787}, {263,3363}, {381,511}, {512,7610}, {1656,6310}, {5650,11287}, {7841,7998}, {11317,11673}
X(12525) = X(6323)-of-McCay-triangle
X(12525) = circumsymmedial-to-McCay similarity image of X(99)
X(12525) = anti-McCay-to-McCay similarity image of X(9879)
The reciprocal orthologic center of these triangles is X(1).
X(12526) lies on these lines: {1,21}, {2,3339}, {8,144}, {9,65}, {10,329}, {19,3958}, {20,6737}, {40,64}, {46,936}, {55,3962}, {56,3928}, {57,960}, {78,165}, {92,4647}, {100,3984}, {145,4314}, {201,2324}, {210,1706}, {219,221}, {377,4312}, {388,527}, {392,3333}, {405,4018}, {452,6738}, {517,3927}, {518,1697}, {519,4294}, {610,1761}, {899,8951}, {908,1698}, {942,10582}, {946,5231}, {950,5698}, {956,7982}, {958,3340}, {962,4847}, {986,2999}, {1001,11518}, {1125,5744}, {1155,5438}, {1158,6282}, {1191,3677}, {1260,5584}, {1376,5128}, {1420,5289}, {1695,3687}, {1699,6734}, {1788,3452}, {1854,7070}, {2263,5279}, {2551,4848}, {2951,9961}, {3057,6762}, {3091,5775}, {3190,4300}, {3218,3361}, {3219,5234}, {3243,3303}, {3338,4880}, {3421,6256}, {3428,7971}, {3434,9589}, {3436,3585}, {3485,5745}, {3556,5285}, {3576,3916}, {3579,3940}, {3601,4640}, {3612,4867}, {3616,10980}, {3617,4866}, {3634,5748}, {3646,5439}, {3680,7285}, {3681,4882}, {3683,5436}, {3698,3715}, {3811,4067}, {3812,7308}, {3827,5227}, {3841,11681}, {3876,8580}, {3885,11519}, {4005,5183}, {4127,8715}, {4298,9965}, {4511,4652}, {4643,5835}, {4668,5176}, {4861,11224}, {5119,5904}, {5219,6668}, {5220,5836}, {5221,5437}, {5252,5857}, {5290,5905}, {5493,6743}, {5552,9588}, {5694,5720}, {5697,10050}, {5705,12047}, {5709,5887}, {5710,7174}, {5794,9579}, {5815,6736}, {5842,5881}, {5884,8726}, {6180,7273}, {6904,12447}, {7688,11517}, {7962,12513}, {9614,10916}, {10527,11522}, {11678,12446}
X(12526) = reflection of X(i) in X(j) for these (i,j): (1,12514), (145,4314), (388,5837), (3340,958), (4295,10), (7982,11496), (9579,5794), (9800,9949)
X(12526) = anticomplement of X(3671)
X(12526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,12514,4512), (8,3951,5223), (40,72,200), (40,5693,1490), (46,5692,936), (55,3962,11523), (57,960,8583), (63,3869,1), (63,11682,2975), (405,4018,11529), (968,2650,1), (1621,11520,1), (2975,3869,11682), (2975,11682,1), (3340,3929,958), (3868,5250,1), (3869,11684,63), (3899,6763,1), (5223,7991,8), (6734,11415,1699)
X(12526) = X(578)-of-inner-Conway-triangle
X(12546) = Conway-circle-inverse of X(37743)
X(12526) = Conway-to-inner-Conway similarity image of X(1)
X(12526) = excentral-to-inner-Conway similarity image of X(12514)
X(12526) = 1st-circumperp-to-excentral similarity image of X(12520)
X(12526) = complement, wrt inner-Conway triangle, of X(12529)
The reciprocal orthologic center of these triangles is X(1).
X(12527) lies on these lines: {1,329}, {2,3361}, {3,6745}, {4,4847}, {8,144}, {9,388}, {10,46}, {12,5745}, {20,200}, {36,6700}, {40,2123}, {56,3452}, {57,2551}, {65,527}, {72,515}, {78,4297}, {100,12512}, {142,10404}, {165,7080}, {191,10039}, {210,7354}, {219,5930}, {226,958}, {355,3927}, {497,6762}, {518,950}, {519,3869}, {529,960}, {535,3678}, {553,3812}, {908,1125}, {936,4293}, {946,956}, {962,4853}, {997,4311}, {1145,3650}, {1210,10629}, {1220,4357}, {1329,3911}, {1697,5698}, {1698,5744}, {1706,3474}, {1737,6763}, {1759,8074}, {1770,3679}, {1788,3928}, {2321,10371}, {2478,11019}, {2550,9579}, {3091,5231}, {3244,11682}, {3245,3626}, {3304,4679}, {3333,5084}, {3338,9843}, {3339,9965}, {3428,6260}, {3475,5436}, {3486,11523}, {3555,11113}, {3600,8583}, {3624,5748}, {3634,11681}, {3671,5905}, {3681,6743}, {3687,6999}, {3697,11112}, {3698,11246}, {3715,9657}, {3717,7270}, {3811,4304}, {3817,10527}, {3868,5850}, {3870,4314}, {3873,6744}, {3876,11678}, {3916,6684}, {3929,9578}, {3962,10950}, {4294,6765}, {4295,9623}, {4353,5262}, {4355,9776}, {4388,9369}, {4643,5793}, {4652,5552}, {4915,9589}, {5022,8568}, {5080,5536}, {5129,10582}, {5220,5794}, {5227,8804}, {5249,5260}, {5252,5837}, {5258,12047}, {5261,5273}, {5265,5328}, {5325,11237}, {5435,8165}, {5534,6868}, {5705,10590}, {5716,7174}, {5730,5882}, {5791,9654}, {5853,6284}, {6904,8580}, {7406,11679}, {10578,11106}, {10860,12246}, {12053,12513}
X(12527) = midpoint of X(i) and X(j) for these {i,j}: {3962,10950}, {5904,10572}
X(12527) = reflection of X(i) in X(j) for these (i,j): (65,5795), (3868,6738), (4292,10), (6737,72), (10106,960)
X(12527) = anticomplement of X(4298)
X(12527) = X(329)-of-inner-Conway-triangle
X(12527) = excentral-to-inner-Conway similarity image of X(10)
X(12527) = Conway-to-inner-Conway similarity image of X(4292)
X(12527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8,144,12526), (20,5815,200), (40,3421,6736), (57,2551,8582), (63,3436,10), (908,2975,1125), (3870,6872,4314), (4652,5552,10164), (5129,11037,10582), (5223,5691,8), (5234,5290,2)
The reciprocal orthologic center of these triangles is X(72).
X(12528) lies on these lines: {1,651}, {3,3219}, {4,912}, {5,9964}, {7,6835}, {8,6001}, {9,6986}, {20,72}, {21,7330}, {33,3562}, {40,3681}, {57,6915}, {63,411}, {65,5229}, {78,84}, {100,1158}, {110,11107}, {119,7705}, {153,355}, {165,3678}, {185,2808}, {200,7992}, {210,9943}, {226,6828}, {255,3465}, {329,6836}, {388,1858}, {392,11106}, {404,5720}, {405,5779}, {443,10861}, {497,1898}, {515,3869}, {516,5904}, {517,3146}, {518,962}, {758,5691}, {908,6245}, {916,5889}, {938,1864}, {942,3091}, {944,3877}, {946,3873}, {952,3885}, {960,5731}, {984,4300}, {997,10085}, {1210,6945}, {1699,3874}, {1709,3811}, {1736,4306}, {1837,9803}, {1854,9370}, {1870,8757}, {1871,6994}, {1902,5921}, {2096,4190}, {2478,5768}, {2800,5881}, {2975,6261}, {3090,10202}, {3100,7078}, {3149,3218}, {3157,6198}, {3305,8726}, {3419,6259}, {3487,6837}, {3523,5044}, {3555,9856}, {3753,9947}, {3839,5806}, {3871,5534}, {3881,11522}, {3889,5603}, {3890,5882}, {3927,7580}, {3935,10306}, {3984,6282}, {4005,5918}, {4015,9588}, {4134,12512}, {4295,7672}, {4297,5692}, {4312,12432}, {4420,10310}, {4511,12114}, {5056,5439}, {5086,6256}, {5174,5906}, {5220,5584}, {5226,6860}, {5249,6991}, {5279,5776}, {5450,6326}, {5531,8715}, {5570,10591}, {5587,5884}, {5658,6838}, {5696,6743}, {5703,6974}, {5728,11036}, {5744,6962}, {5758,10431}, {5770,6834}, {5787,6840}, {5812,6895}, {5817,6886}, {5883,7989}, {6147,8226}, {6260,6734}, {6888,11374}, {6938,11015}, {7282,7331}, {7414,9928}, {7548,9612}, {7987,10176}, {8095,11690}, {8227,12005}, {8581,11037}, {9948,11678}, {10303,11227}, {10826,11570}, {11444,11573}
X(12528) = reflection of X(i) in X(j) for these (i,j): (20,72), (944,5887), (3555,9856), (3868,4), (3869,5693), (9960,1490), (9961,40)
X(12528) = X(68)-of-inner-Conway-triangle
X(12528) = excentral-to-inner-Conway similarity image of X(1490)
X(12528) = Conway-to-inner-Conway similarity image of X(9960)
X(12528) = inner-Conway-isotomic conjugate of X(12530)
X(12528) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9,10884,6986), (63,1490,411), (78,84,6909), (329,9799,6836), (908,6245,6943), (942,5927,3091), (944,5887,3877), (3681,9961,40), (3876,11220,3), (5044,10167,3523), (5439,10157,5056)
The reciprocal orthologic center of these triangles is X(65).
X(12529) lies on these lines: {8,6001}, {63,7992}, {65,5175}, {72,6361}, {100,3876}, {224,1621}, {329,9800}, {516,3869}, {758,3632}, {912,5082}, {1858,2550}, {1898,2551}, {2801,4853}, {2975,10085}, {3434,3868}, {3671,3873}, {3681,4882}, {3877,4294}, {3890,4314}, {4511,11496}, {4512,4855}, {5086,10573}, {5174,6327}, {5744,9943}, {5777,7080}, {9949,11678}
X(12529) = reflection of X(3868) in X(4295)
X(12529) = anticomplement, wrt inner-Conway triangle, of X(12526)
X(12529) = {X(4882), X(12059)}-harmonic conjugate of X(3681)
The reciprocal orthologic center of these triangles is X(65).
X(12530) lies on these lines: {63,1721}, {100,1766}, {200,7996}, {329,9801}, {516,3869}, {990,2975}, {1633,1760}, {1742,1959}, {3663,3873}, {3681,3729}, {3876,3923}, {5744,9944}, {9950,11678}
X(12530) = reflection of X(9962) in X(1721)
X(12530) = X(317)-of-inner-Conway-triangle
X(12530) = excentral-to-inner-Conway similarity image of X(1721)
X(12530) = inner-Conway-isotomic conjugate of X(12528)
X(12530) = anticomplement, wrt inner-Conway triangle, of X(3729)
The reciprocal orthologic center of these triangles is X(8).
X(12531) lies on these lines: {1,6702}, {2,1317}, {3,8}, {10,7972}, {11,145}, {21,10087}, {63,4677}, {78,6264}, {80,519}, {119,11680}, {144,528}, {149,3436}, {153,3434}, {200,7993}, {214,3679}, {329,9802}, {355,10698}, {404,10074}, {517,10724}, {1156,5853}, {1387,3241}, {2771,10914}, {2800,5881}, {2802,3632}, {3035,3617}, {3555,6797}, {3622,6667}, {3625,11684}, {3871,10058}, {4193,5533}, {4853,5531}, {4861,6265}, {5080,5844}, {5253,10944}, {5818,11729}, {5840,12245}, {5846,10755}, {6713,7967}, {6735,10265}, {8097,11690}, {8197,12461}, {8204,12460}, {9951,11678}, {11362,12119}
X(12531) = midpoint of X(i) and X(j) for these {i,j}: {149,3621}, {3632,9897}
X(12531) = reflection of X(i) in X(j) for these (i,j): (100,8), (145,11), (1317,3036), (1320,80), (3555,6797), (6224,1145), (7972,10), (9963,5541), (10031,3679), (10698,355), (12119,11362)
X(12531) = anticomplement of X(1317)
X(12531) = X(74)-of-inner-Conway-triangle
X(12531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8,6224,1145), (80,1320,10707), (956,12331,4996), (1145,6224,100), (1317,3036,2), (4996,12331,100)
The reciprocal orthologic center of these triangles is X(3869).
X(12532) lies on these lines: {2,11570}, {8,153}, {10,11571}, {11,3868}, {63,4996}, {72,74}, {78,1768}, {80,758}, {104,912}, {144,2801}, {149,11415}, {214,5692}, {329,9803}, {517,10724}, {518,1156}, {908,10265}, {952,3869}, {1145,3681}, {1317,3877}, {1387,3873}, {2802,3621}, {2829,12528}, {2932,3940}, {2975,5694}, {3035,3876}, {3218,10090}, {3436,12247}, {3616,5083}, {3648,4127}, {3878,7972}, {4018,6797}, {4861,5887}, {5046,10073}, {5057,10738}, {5086,10742}, {5531,12526}, {5744,9946}, {5902,6702}, {6264,11682}, {9952,11678}
X(12532) = reflection of X(i) in X(j) for these (i,j): (100,72), (3868,11), (4018,6797), (6265,5694), (7972,3878), (9964,6326), (10698,5887), (11571,10)
X(12532) = anticomplement of X(11570)
X(12532) = {X(63), X(6326)}-harmonic conjugate of X(4996)
X(12532) = X(265)-of-inner-Conway-triangle
X(12532) = excentral-to-inner-Conway similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3555).
X(12533) lies on these lines: {8,6835}, {100,12516}, {145,5920}, {200,8001}, {329,9804}, {2975,12521}, {5744,12439}, {9953,11678}
X(12533) = reflection of X(145) in X(5920)
X(12533) = excentral-to-inner-Conway similarity image of X(12658)
The reciprocal orthologic center of these triangles is X(3555).
X(12534) lies on these lines: {4,6735}, {100,12517}, {2975,12522}, {3729,5082}, {5744,12442}, {11678,12449}
The reciprocal orthologic center of these triangles is X(21).
X(12535) lies on these lines: {2,10044}, {100,12519}, {191,7161}, {2975,12524}, {3648,4127}, {5744,12444}, {11678,12451}
X(12535) = reflection of X(10266) in X(191)
The reciprocal orthologic center of these triangles is X(1).
X(12536) lies on these lines: {1,4208}, {2,12437}, {7,145}, {8,21}, {20,519}, {35,5775}, {63,2136}, {78,5328}, {80,5828}, {377,3241}, {390,6737}, {474,938}, {517,9960}, {527,5059}, {944,6764}, {952,9799}, {1004,4308}, {2802,9964}, {2900,5175}, {3146,11523}, {3158,3617}, {3244,11036}, {3419,5703}, {3434,4323}, {3476,9797}, {3488,11108}, {3623,5249}, {3632,4304}, {3633,4292}, {3813,4197}, {3868,3880}, {3893,10391}, {4188,5435}, {4853,7675}, {4866,6743}, {5260,6600}, {5440,5704}, {5731,8666}, {5732,11519}, {5734,6839}, {5794,10578}, {5815,10572}, {5836,11020}, {5854,9963}, {6172,6872}, {7411,12513}, {10861,12448}
X(12536) = reflection of X(i) in X(j) for these (i,j): (8,3189), (3146,11523), (3621,2136), (6764,944)
X(12536) = X(64)-of-Conway-triangle
X(12536) = X(6293)-of-2nd-Conway-triangle
X(12536) = excentral-to-Conway similarity image of X(2136)
X(12536) = excentral-to-2nd-Conway similarity image of X(12625)
X(12536) = orthologic center of these triangles: Conway to 2nd Schiffler
X(12536) = {X(8), X(4313)}-harmonic conjugate of X(5273)
The reciprocal orthologic center of these triangles is X(3555).
X(12537) lies on these lines: {2,12439}, {7,3555}, {21,3870}, {63,12533}, {3681,12260}, {4313,5920}, {5732,8001}, {7411,12516}, {9953,10861}
X(12537) = reflection of X(9874) in X(3555)
The reciprocal orthologic center of these triangles is X(3555).
X(12538) lies on these lines: {2,12442}, {21,12522}, {63,12534}, {1266,6361}, {7411,12517}, {10861,12449}
The reciprocal orthologic center of these triangles is X(1).
X(12539) lies on these lines: {1,11888}, {2,12443}, {7,177}, {21,12523}, {63,164}, {167,5732}, {4313,8422}, {5571,11020}, {7411,12518}, {8080,8733}, {10861,12450}
X(12539) = reflection of X(i) in X(j) for these (i,j): (9807,177), (11691,164)
X(12539) = orthologic center of these triangles: Conway to 2nd midarc
X(12539) = X(1)-of-Conway-triangle
X(12539) = {X(11888), X(11889)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(21).
X(12540) lies on these lines: {2,12444}, {7,6597}, {20,5538}, {21,10266}, {63,12535}, {1836,3868}, {5905,12536}, {7411,12519}, {10861,12451}
The reciprocal orthologic center of these triangles is X(1).
X(12541) lies on these lines: {1,11024}, {2,2136}, {7,145}, {8,210}, {65,9797}, {72,9804}, {78,4345}, {329,3621}, {390,4853}, {516,11519}, {517,6764}, {519,962}, {938,10914}, {1697,5273}, {2802,9803}, {3158,3622}, {3169,5296}, {3189,3241}, {3244,11037}, {3616,3913}, {3632,5815}, {3633,4295}, {3811,5734}, {3813,9780}, {3870,4323}, {4298,12127}, {4342,4882}, {4513,5838}, {5176,7319}, {5274,6736}, {5328,12053}, {5758,5844}, {5828,10591}, {5836,10580}, {5854,9802}, {6601,7320}, {7674,8236}, {9778,12513}, {10578,11281}
X(12541) = reflection of X(i) in X(j) for these (i,j): (145,3680), (3057,12448), (3189,10912), (12536,145)
X(12541) = anticomplement of X(2136)
X(12541) = orthologic center of these triangles: 2nd Conway to 2nd Schiffler
X(12541) = X(64)-of-2nd-Conway-triangle
X(12541) = excentral-to-2nd-Conway similarity image of X(2136)
X(12541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497,3893,8), (3189,10912,3241)
The reciprocal orthologic center of these triangles is X(3555).
X(12542) lies on these lines: {7,12538}, {8,12449}, {329,12534}, {3616,12522}, {3935,5758}, {9776,12442}, {9778,12517}
X(12542) = anticomplement of X(12659)
The reciprocal orthologic center of these triangles is X(21).
X(12543) lies on these lines: {7,6597}, {8,10266}, {329,12535}, {2476,9782}, {3616,12524}, {5046,6599}, {9776,12444}, {9778,12519}, {9799,10525}, {9802,10912}
X(12543) = anticomplement of X(12660)
The reciprocal orthologic center of these triangles is X(1).
X(12544) lies on these lines: {1,7}, {10,10888}, {40,7413}, {758,12435}, {1125,10856}, {1330,5691}, {1695,4384}, {1709,10461}, {1722,9535}, {1764,12514}, {3841,10887}, {5208,9961}, {5248,10882}, {6001,10441}, {9800,10453}, {10434,12511}, {10862,12446}, {11679,12526}
X(12544) = X(578)-of-3rd-Conway-triangle
X(12544) = excentral-to-3rd-Conway similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12545) lies on these lines: {1,7}, {4,3741}, {10,1764}, {40,3980}, {515,10441}, {519,12126}, {894,2944}, {946,4425}, {950,10473}, {978,9535}, {1125,10478}, {3146,10453}, {3244,11521}, {3634,10887}, {5247,6996}, {5691,10449}, {6744,11021}, {7406,11679}, {10106,10480}, {10434,12512}, {10439,10454}, {10452,10464}, {10475,12053}, {10856,12436}, {10862,12447}
X(12545) = Conway circle-inverse-of-X(5018)
X(12545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10442,12544), (4,10476,3741), (10446,10465,1), (10478,10882,1125)
X(12545) = X(389)-of-3rd-Conway-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12546) lies on these lines: {1,2}, {740,11531}, {1764,2136}, {3680,10435}, {3813,10887}, {3880,12435}, {3893,10473}, {3913,10882}, {5836,11021}, {5853,10442}, {10434,12513}, {10444,12536}, {10446,12541}, {10856,12437}, {10862,12448}, {10912,11369}
X(12546) = orthologic center of these triangles: 3rd Conway to 2nd Schiffler
X(12546) = X(64)-of-3rd-Conway-triangle
X(12546) = excentral-to-3rd-Conway similarity image of X(2136)
The reciprocal orthologic center of these triangles is X(72).
X(12547) lies on these lines: {1,84}, {4,10435}, {515,12435}, {517,12546}, {944,10890}, {946,11021}, {971,10441}, {1158,10434}, {1490,1764}, {5691,10825}, {6245,10478}, {6260,10479}, {6261,10882}, {9799,10446}, {9942,10856}, {9948,10862}, {9960,10444}, {11679,12528}
X(12547) = X(68)-of-3rd-Conway-triangle
X(12547) = excentral-to-3rd-Conway similarity image of X(1490)
X(12547) = 3rd-Conway-isotomic conjugate of X(12549)
The reciprocal orthologic center of these triangles is X(65).
X(12548) lies on these lines: {1,84}, {516,10454}, {3671,11021}, {4512,10470}, {9800,10446}, {9943,10856}, {9949,10862}, {9961,10444}, {10434,12514}, {10439,12544}, {10882,12520}, {11679,12529}
X(12548) = excentral-to-3rd-Conway similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12549) lies on these lines: {1,7175}, {516,10454}, {968,1766}, {990,10882}, {1721,1764}, {3663,11021}, {3729,3869}, {4061,10445}, {5208,9962}, {9801,10446}, {9944,10856}, {9950,10862}, {11679,12530}
X(12549) = X(317)-of-3rd-Conway-triangle
X(12549) = excentral-to-3rd-Conway similarity image of X(1721)
X(12549) = 3rd-Conway-isotomic conjugate of X(12547)
X(12549) = anticomplement, wrt 3rd Conway triangle, of X(10444)
The reciprocal orthologic center of these triangles is X(8).
X(12550) lies on these lines: {1,5}, {100,10882}, {104,10434}, {528,10442}, {1320,10435}, {1764,5541}, {2800,12547}, {2802,12435}, {5854,12546}, {8097,11894}, {9802,10446}, {9945,10856}, {9951,10862}, {9963,10444}, {10825,11521}, {11679,12531}
X(12550) = Conway circle-inverse-of-X(1317)
X(12550) = X(74)-of-3rd-Conway-triangle
X(12550) = excentral-to-3rd-Conway similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(3869).
X(12551) lies on these lines: {1,104}, {11,11369}, {80,10435}, {517,12550}, {952,12435}, {1387,11021}, {1764,6326}, {2771,10441}, {2801,10442}, {2802,12546}, {2829,12547}, {6264,11521}, {6265,10882}, {7972,10890}, {9803,10446}, {9809,10449}, {9897,10825}, {9946,10856}, {9952,10862}, {9964,10444}, {10265,10478}, {10434,12515}, {11679,12532}
X(12551) = Conway circle-inverse-of-X(11700)
X(12551) = X(265)-of-3rd-Conway-triangle
X(12551) = excentral-to-3rd-Conway similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3555).
X(12552) lies on these lines: {1,5920}, {9804,10446}, {9953,10862}, {10434,12516}, {10444,12537}, {10856,12439}, {10882,12521}, {11679,12533}
The reciprocal orthologic center of these triangles is X(3555).
X(12553) lies on these lines: {1266,6361}, {10434,12517}, {10446,12542}, {10856,12442}, {10862,12449}, {10882,12522}, {11679,12534}
The reciprocal orthologic center of these triangles is X(1).
X(12554) lies on these lines: {1,167}, {164,1764}, {5571,11021}, {7670,10889}, {9807,10446}, {10434,12518}, {10444,12539}, {10856,12443}, {10862,12450}, {10882,12523}, {11679,11691}
X(12554) = orthologic center of these triangles: 3rd Conway to 2nd midarc
X(12554) = X(1)-of-3rd-Conway-triangle
X(12554) = {X(11894),X(11895)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(1).
X(12555) lies on these lines: {1,3}, {329,4416}, {511,1750}, {527,10442}, {966,3452}, {1396,1753}, {1999,9965}, {3781,8580}, {3820,10887}, {7682,10479}, {7956,10886}, {8101,11894}, {9954,10862}
X(12555) = Conway circle-inverse-of-X(3660)
X(12555) = X(25)-of-3rd-Conway-triangle
X(12555) = excentral-to-3rd-Conway similarity image of X(57)
X(12555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1764,10856), (10446,11679,10888)
The reciprocal orthologic center of these triangles is X(79)
X(12556) lies on these lines: {2,12600}, {3,10266}, {4,13089}, {20,5694}, {30,12798}, {35,13128}, {36,13129}, {40,12660}, {56,13080}, {100,3648}, {165,12409}, {182,12209}, {376,12255}, {515,12786}, {517,13100}, {1593,12146}, {2771,12535}, {3098,12504}, {3576,12267}, {3651,12519}, {5732,12845}, {5840,6595}, {6284,12957}, {7354,12947}, {10310,12342}, {11248,13130}, {11249,13131}, {11414,12414}, {11822,12482}, {11823,12483}, {11824,12807}, {11825,12808}, {11826,12927}, {11827,12937}, {11829,13001}
X(12556) = reflection of X(i) in X(j) for these (i,j): (4,13089), (10266,3)
X(12556) = anticomplement of X(12600)
X(12556) = X(10266)-of-ABC-X3-reflections-triangle
The reciprocal orthologic center of these triangles is X(21).
X(12557) lies on these lines: {1,5180}, {6597,10435}, {10434,12519}, {10444,12540}, {10446,12543}, {10856,12444}, {10862,12451}, {10882,12524}, {11679,12535}
The reciprocal orthologic center of these triangles is X(1).
X(12558) lies on these lines: {1,10883}, {2,12511}, {4,3822}, {5,516}, {10,7957}, {11,3671}, {12,4314}, {35,6894}, {40,6990}, {165,6991}, {226,1898}, {758,946}, {1699,5705}, {3814,5537}, {3817,3825}, {3925,5493}, {4294,7951}, {4295,5704}, {4421,11496}, {5885,6001}, {8227,12520}, {10395,12432}, {11680,12526}
X(12558) = midpoint of X(4) and X(5248)
X(12558) = reflection of X(3841) in X(5)
X(12558) = complement of X(12511)
X(12558) = X(578)-of-3rd-Euler-triangle
X(12558) = excentral-to-3rd-Euler similarity image of X(12514)
X(12558) = {X(3817), X(6831)}-harmonic conjugate of X(3825)
The reciprocal orthologic center of these triangles is X(1).
X(12559) lies on these lines: {1,21}, {9,4067}, {10,3487}, {40,4084}, {55,4018}, {65,3689}, {72,3715}, {78,5902}, {145,4295}, {200,3754}, {214,3361}, {354,5730}, {377,11551}, {388,519}, {405,3962}, {516,944}, {517,12520}, {936,5883}, {942,997}, {1125,11518}, {1159,5836}, {1482,6001}, {1698,3984}, {1706,3919}, {2093,4757}, {2099,3555}, {3158,4744}, {3218,3612}, {3241,4294}, {3336,4855}, {3338,4511}, {3419,3649}, {3485,10916}, {3635,4314}, {3679,3841}, {3711,4002}, {3812,3940}, {3928,5267}, {3951,5251}, {4301,7971}, {4305,9965}, {4333,11015}, {4430,4861}, {4652,4880}, {4917,5541}, {4930,7373}, {4973,7987}, {5045,5289}, {5221,5440}, {5425,5904}, {5791,11281}, {5794,6147}, {5905,10572}, {6668,11374}, {7991,12511}, {9851,11224}, {11519,12446}, {11521,12544}, {11522,12558}
X(12559) = X(578)-of-excenters-reflections-triangle
X(12559) = excentral-to-excenters-reflections similarity image of X(12514)
X(12559) = midpoint of X(145) and X(4295)
X(12559) = reflection of X(i) in X(j) for these (i,j): (4314,3635), (5794,6147), (7991,12511), (12514,1), (12526,5248)
X(12559) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,3901,63), (1,12526,5248), (3243,7982,3244), (4757,8715,2093), (5248,12526,12514), (11523,11529,10)
The reciprocal orthologic center of these triangles is X(1).
X(12560) lies on these lines: {1,7}, {9,65}, {10,8232}, {40,954}, {57,1001}, {85,3886}, {142,3485}, {200,226}, {388,5853}, {480,1706}, {518,3340}, {528,4654}, {673,2258}, {758,5223}, {942,3358}, {948,3755}, {1125,8732}, {1159,5779}, {1445,3339}, {1449,1456}, {1768,10980}, {1788,6666}, {2099,3243}, {3059,11523}, {3062,10394}, {3333,11496}, {3361,5248}, {3475,10388}, {3487,6769}, {3601,11495}, {3826,5219}, {3841,7679}, {3883,6604}, {4882,5261}, {5045,7171}, {5226,8580}, {5228,7290}, {5290,6765}, {5572,10384}, {5728,6001}, {5809,6738}, {7091,10390}, {7673,9819}, {7676,12511}, {7678,12558}, {10860,11018}, {10865,12446}, {11520,12529}, {11526,12559}
X(12560) = reflection of X(i) in X(j) for these (i,j): (7,3671), (2951,12520), (4326,1), (12526,9)
X(12560) = X(578)-of-Honsberger-triangle
X(12560) = excentral-to-Honsberger similarity image of X(12514)
X(12560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,7,4321), (1,2951,7675), (1,4312,5732), (1,7271,1458), (1,7274,4327), (7,4323,11038), (7,8236,3600), (2099,8581,3243), (4318,7190,1), (7672,8545,5223), (10384,11518,5572), (11372,11529,5728)
The reciprocal orthologic center of these triangles is X(1).
X(12561) lies on these lines: {1,11886}, {10,5934}, {363,12514}, {516,9836}, {758,9805}, {1125,11854}, {3671,8113}, {3841,8380}, {4295,9783}, {4314,8390}, {5248,8109}, {8107,12511}, {8111,12520}, {8385,12560}, {11527,12559}, {11685,12526}, {11856,12446}, {11892,12544}
X(12561) = X(578)-of-inner-Hutson-triangle
X(12561) = excentral-to-inner-Hutson similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12562) lies on these lines: {1,11887}, {10,5935}, {516,9837}, {758,9806}, {1125,11855}, {3671,8114}, {3841,8381}, {4295,9787}, {4314,8392}, {5248,8110}, {8108,12511}, {8112,12520}, {8140,12561}, {8378,12558}, {8386,12560}, {11528,12559}, {11686,12526}, {11857,12446}, {11893,12544}
X(12562) = X(578)-of-outer-Hutson-triangle
X(12562) = excentral-to-outer-Hutson similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12563) lies on these lines: {1,7}, {10,3487}, {142,12447}, {226,1837}, {495,3626}, {496,12558}, {515,6147}, {519,5794}, {551,3333}, {553,2646}, {758,942}, {938,3817}, {946,5787}, {950,3649}, {958,5850}, {999,3636}, {1056,3244}, {1159,11362}, {1210,10171}, {3295,12511}, {3339,5703}, {3340,3475}, {3485,11019}, {3486,4654}, {3616,10980}, {3622,4512}, {3625,11041}, {3634,11374}, {3982,7354}, {4031,5204}, {4847,11520}, {5045,6001}, {5249,6737}, {5572,9856}, {5708,10165}, {5719,6684}, {5789,5886}, {5880,12437}, {5883,6700}, {6598,11263}, {7373,11496}, {7991,10578}, {10569,10866}, {10580,11522}, {11035,12446}, {11039,12561}, {11040,12562}
X(12563) = midpoint of X(i) and X(j) for these {i,j}: {1,3671}, {10,12559}, {4295,4314}, {4301,12520}
X(12563) = reflection of X(i) in X(j) for these (i,j): (3626,3841), (5248,3636)
X(12563) = X(578)-of-incircle-circles-triangle
X(12563) = excentral-to-incircle-circles similarity image of X(12514)
X(12563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,7,4297), (1,4295,4314), (1,4312,4313), (1,4355,5731), (1,11036,5542), (1,11551,4292), (3339,5703,10164), (3485,11518,11019), (3487,11529,10), (3671,4314,4295), (4323,11038,1), (5745,11281,1125)
The reciprocal orthologic center of these triangles is X(1).
X(12564) lies on these lines: {1,21}, {10,3059}, {55,12432}, {57,12511}, {65,4314}, {226,1898}, {354,3671}, {516,942}, {938,5883}, {1125,11018}, {1210,3833}, {1864,3947}, {3085,4015}, {3333,12520}, {3339,4326}, {3754,6738}, {4208,5696}, {4294,5902}, {4295,10580}, {4298,10391}, {4355,11220}, {5045,6001}, {5290,10394}, {5703,10176}, {5842,12433}, {5884,11496}, {5904,10578}, {8255,8728}, {9949,10569}, {11019,12446}, {11021,12544}, {11025,12560}, {11026,12561}, {11027,12562}
X(12564) = midpoint of X(i) and X(j) for these {i,j}: {65,4314}, {3874,12514}, {5884,11496}
X(12564) = reflection of X(12563) in X(5045)
X(12564) = X(578)-of-inverse-in-incircle-triangle
X(12564) = excentral-to-inverse-in-incircle similarity image of X(12514)
X(12564) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,774,3743), (942,5572,6744)
The reciprocal orthologic center of these triangles is X(1).
Let A' be the trilinear product of the circumcircle intercepts of the A-excircle. Define B' and C' cyclically. Triangle A'B'C' is perspective to the excentral triangle at X(12565). (Randy Hutson, July 31 2018)
X(12565) lies on these lines: {1,7}, {2,9800}, {3,4512}, {9,5584}, {10,1750}, {40,64}, {56,5918}, {57,9943}, {63,7992}, {78,9778}, {84,3428}, {165,411}, {221,7070}, {255,2956}, {497,1467}, {515,4853}, {610,3556}, {758,6765}, {946,8726}, {956,10864}, {960,11495}, {997,12512}, {1103,1745}, {1125,10857}, {1245,2999}, {1764,12548}, {2093,12432}, {3062,5234}, {3174,7957}, {3333,10167}, {3555,6766}, {3576,11496}, {3579,5720}, {3587,5887}, {3811,5493}, {4847,9799}, {5223,12528}, {5231,6245}, {5248,7987}, {5691,9623}, {6261,6282}, {6361,6769}, {7171,11249}, {8580,9949}, {10980,12564}, {11531,12559}
X(12565) = midpoint of X(i) and X(j) for these {i,j}: {9961,12529}, {12561,12562}
X(12565) = reflection of X(i) in X(j) for these (i,j): (1,12520), (962,3671), (4294,4297), (4326,5732), (11531,12559), (12514,12511), (12526,40)
X(12565) = complement of X(9800)
X(12565) = X(578)-of-6th-mixtilinear-triangle
X(12565) = excentral-to-6th-mixtilinear similarity image of X(12514)
X(12565) = 2nd-extouch-to-hexyl similarity image of X(40)
X(12565) = 2nd-circumperp-to-excentral similarity image of X(12520)
X(12565) = anticomplement, wrt excentral triangle, of X(12514)
X(12565) = orthologic center of these triangles: excentral to 4th extouch
X(12565) = Ursa-minor-to-excentral similarity image of X(17634)
X(12565) = Ursa-major-to-excentral similarity image of X(17650)
X(12565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1044,269), (1,2951,20), (1,4295,12560), (40,1490,200), (56,5918,9841), (63,9961,7992), (946,8726,10582), (962,10884,1), (1042,4319,1), (3811,5493,7994), (12511,12514,165)
The reciprocal orthologic center of these triangles is X(1).
X(12566) lies on these lines: {1,10885}, {3,142}, {10,8233}, {758,9808}, {3671,8243}, {3841,8230}, {4295,9789}, {4314,8239}, {6001,12490}, {8228,12558}, {8231,12514}, {8234,12520}, {8237,12560}, {10867,12446}, {10891,12544}, {11030,12564}, {11042,12563}, {11532,12559}, {11687,12526}
X(12566) = X(578)-of-2nd-Pamfilos-Zhou-triangle
X(12566) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12567) lies on these lines: {1,21}, {10,4199}, {56,10180}, {740,958}, {1284,3671}, {4068,12513}, {4295,9791}, {4314,8240}, {4647,5251}, {6001,9959}, {8235,12520}, {8238,12560}, {11043,12563}, {11926,12562}
X(12567) = X(578)-of-1st-Sharygin-triangle
X(12567) = excentral-to-1st-Sharygin similarity image of X(12514)
X(12567) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13245)
The reciprocal orthologic center of these triangles is X(1).
X(12568) lies on these lines: {1,11888}, {10,8079}, {516,8091}, {758,8093}, {1125,8733}, {2089,3671}, {3841,8087}, {4295,9793}, {4314,8241}, {5248,8077}, {6001,8099}, {8075,12511}, {8078,12514}, {8081,12520}, {8085,12558}, {8089,12565}, {8133,12561}, {8135,12562}, {8249,12567}, {8387,12560}, {11032,12564}, {11690,12526}, {11894,12544}
X(12568) = X(578)-of-tangential-midarc-triangle
X(12568) = excentral-to-tangential-midarc similarity image of X(12514)
X(12568) = reflection of X(12569) in X(1)
The reciprocal orthologic center of these triangles is X(1).
X(12569) lies on these lines: {1,11888}, {10,8080}, {516,8092}, {758,8094}, {3841,8088}, {4295,9795}, {4314,8242}, {6001,8100}, {8076,12511}, {8082,12520}, {8086,12558}, {8090,12565}, {8138,12562}, {8248,12566}, {8250,12567}, {8388,12560}, {11033,12564}, {11895,12544}
X(12569) = reflection of X(12568) in X(1)
X(12569) = X(578)-of-2nd-tangential-midarc-triangle
X(12569) = excentral-to-2nd-tangential-midarc similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12570) lies on these lines: {1,11890}, {174,3671}, {516,8351}, {758,12445}, {1125,8729}, {3841,8382}, {4295,11891}, {4314,11924}, {5248,7587}, {6001,12491}, {8083,12564}, {8126,12526}, {8423,12565}, {8425,12567}, {11535,12559}, {11860,12446}, {11896,12544}, {11996,12566}
X(12570) = X(578)-of-Yff-central-triangle
X(12570) = excentral-to-Yff-central similarity image of X(12514)
The reciprocal orthologic center of these triangles is X(1).
X(12571) lies on these lines: {1,3832}, {2,10248}, {3,10171}, {4,1125}, {5,516}, {8,3854}, {10,962}, {11,4298}, {20,7988}, {40,3545}, {165,5056}, {226,6744}, {355,519}, {497,3947}, {515,3636}, {517,4015}, {551,5691}, {758,5806}, {908,5178}, {1698,5493}, {3244,11522}, {3626,4301}, {3635,5603}, {3671,9581}, {3678,10157}, {3825,12436}, {3833,9943}, {3874,5927}, {3911,7173}, {4292,7741}, {4312,5704}, {4314,5219}, {4315,5229}, {4342,9578}, {4347,9817}, {4669,11531}, {4701,7982}, {4745,5818}, {5274,5290}, {5425,6738}, {5542,5714}, {5715,5811}, {5722,12563}, {5726,9785}, {5789,5805}, {7951,10624}, {9579,10589}, {9580,10588}, {9589,9780}, {9612,10591}, {9614,10590}, {10895,12053}, {11680,12527}
X(12571) = midpoint of X(i) and X(j) for these {i,j}: {4,1125}, {546,9955}, {3626,4301}, {3754,9856}, {4701,7982}
X(12571) = reflection of X(3634) in X(5)
X(12571) = complement of X(12512)
X(12571) = X(389)-of-3rd-Euler-triangle
X(12571) = 2nd-Conway-to-excentral similarity image of X(12512)
X(12571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,3817,1125), (4,8227,4297), (5,3579,10172), (962,3091,7989), (962,7989,10), (1698,9812,5493), (1699,3091,10), (1699,7989,962), (3817,4297,8227), (3832,9779,1), (4297,8227,1125), (4301,5587,3626), (5068,9812,1698), (5219,5225,4314), (9612,10591,11019)
The reciprocal orthologic center of these triangles is X(1).
X(12572) lies on these lines: {1,329}, {2,4292}, {3,3452}, {4,9}, {5,5745}, {7,5129}, {8,3586}, {12,3683}, {20,936}, {21,908}, {30,5044}, {35,1005}, {37,5717}, {44,1834}, {46,8582}, {56,226}, {57,5084}, {63,1210}, {72,519}, {78,4304}, {84,6865}, {142,11108}, {144,938}, {191,1737}, {200,4294}, {201,1877}, {204,7952}, {210,6284}, {355,5837}, {376,5438}, {377,3305}, {381,5325}, {387,1743}, {390,5815}, {392,10106}, {440,3454}, {442,1155}, {443,7308}, {474,5316}, {515,960}, {517,5795}, {522,11247}, {527,942}, {528,4662}, {551,3487}, {553,5439}, {758,6738}, {846,5530}, {946,958}, {956,12053}, {962,9623}, {997,1490}, {1006,5267}, {1058,6762}, {1104,4415}, {1167,1785}, {1260,8715}, {1329,4640}, {1330,3912}, {1479,4847}, {1697,3421}, {1698,1770}, {1699,5234}, {1901,4205}, {2049,5257}, {2321,5814}, {2325,3695}, {2816,3042}, {2886,5302}, {3085,4512}, {3091,5273}, {3219,5046}, {3244,3488}, {3419,3626}, {3436,5250}, {3523,5328}, {3579,3820}, {3601,11111}, {3678,6743}, {3679,5175}, {3686,5295}, {3687,7283}, {3710,5016}, {3717,5015}, {3811,4314}, {3817,5715}, {3868,10399}, {3874,5728}, {3876,11114}, {3883,4385}, {3911,3916}, {3927,5722}, {3929,9581}, {3940,12437}, {3947,10198}, {4186,7085}, {4199,6685}, {4222,5285}, {4293,8583}, {4301,5758}, {4357,4911}, {4387,10371}, {4416,10449}, {4703,5928}, {4863,9670}, {4999,5087}, {5047,5249}, {5051,5294}, {5057,5260}, {5082,9580}, {5119,6736}, {5219,6857}, {5223,5809}, {5231,10591}, {5251,12047}, {5289,5882}, {5290,8232}, {5692,6737}, {5703,11106}, {5709,6893}, {5720,6868}, {5744,6919}, {5762,5806}, {5779,5787}, {5927,10176}, {6245,6827}, {6666,8728}, {6705,6922}, {6832,10171}, {6908,10164}, {6920,11813}, {6992,10884}, {7007,8806}, {7082,10953}, {7580,12512}, {8226,12571}, {8983,9678}, {9841,12246}, {10888,12545}
X(12572) = midpoint of X(i) and X(j) for these {i,j}: {1,12527}, {8,10624}, {72,950}, {6737,10572}
X(12572) = reflection of X(i) in X(j) for these (i,j): (3874,6744), (4292,12436), (4298,1125), (6743,3678)
X(12572) = anticomplement of X(12436)
X(12572) = complement of X(4292)
X(12572) = X(389)-of-2nd-extouch-triangle
X(12572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,4292,12436), (3,3452,6700), (4,9,10), (40,2551,10), (57,5084,9843), (63,2478,1210), (72,11113,950), (78,6872,4304), (226,405,1125), (329,452,1), (390,5815,6765), (1329,4640,6684), (1490,6987,4297), (2551,5698,40), (3091,5273,5705), (3219,5046,6734), (3487,5436,551), (3488,11523,3244), (5812,6913,946), (7308,9579,443)
The reciprocal orthologic center of these triangles is X(1).
X(12573) lies on these lines: {1,7}, {9,388}, {10,1445}, {12,6666}, {56,142}, {57,2550}, {65,5853}, {85,3883}, {226,1001}, {278,1890}, {515,5728}, {518,4032}, {519,7672}, {527,5434}, {528,553}, {673,1416}, {948,7290}, {950,5572}, {999,5805}, {1056,5759}, {1125,7677}, {1471,3008}, {2257,5819}, {3243,3476}, {3244,11526}, {3361,8732}, {3634,7679}, {3755,5228}, {3826,3911}, {3886,6604}, {4067,5850}, {4989,5723}, {5263,9436}, {5269,7365}, {5290,8232}, {5691,5809}, {5716,7273}, {6594,10956}, {6601,7091}, {6744,11025}, {7676,12512}, {7678,12571}, {9579,10384}, {9613,10398}, {10865,12447}
X(12573) = reflection of X(i) in X(j) for these (i,j): (7,4298), (950,5572), (12527,9)
X(12573) = X(389)-of-Honsberger-triangle
X(12573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7,390,12560), (7,3600,4321), (7,4308,11038), (4327,4331,3663)
The reciprocal orthologic center of these triangles is X(1).
X(12574) lies on these lines: {1,9783}, {10,363}, {20,8140}, {3244,11527}, {4292,11886}, {4297,8111}, {4298,8113}, {5934,12572}, {6744,11026}, {8107,12512}, {8385,12573}, {11685,12527}, {11856,12447}, {11892,12545}
X(12574) = X(389)-of-inner-Hutson-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12575) lies on these lines: {1,7}, {8,4082}, {10,497}, {11,3634}, {12,12571}, {30,10105}, {40,1058}, {55,474}, {56,12512}, {57,5493}, {65,6744}, {72,519}, {144,9797}, {145,12527}, {226,3303}, {388,9580}, {392,10866}, {452,4853}, {496,6684}, {498,10171}, {515,9856}, {517,6738}, {551,3601}, {726,11997}, {938,7991}, {946,3295}, {960,5853}, {1000,5881}, {1191,3755}, {1210,5119}, {1385,10386}, {1479,6957}, {1617,12511}, {1698,5274}, {1699,3947}, {1837,3626}, {2098,3635}, {2136,2551}, {2269,3294}, {2478,3895}, {2646,3636}, {3085,3817}, {3086,10164}, {3244,3486}, {3333,6361}, {3339,10580}, {3361,9778}, {3452,3913}, {3485,10389}, {3488,7982}, {3555,5850}, {3621,8275}, {3624,5281}, {3625,5727}, {3718,3883}, {3746,5443}, {3811,10388}, {3813,5745}, {3828,11238}, {3832,5726}, {3871,6745}, {3877,6737}, {3880,5795}, {3881,10391}, {4652,11240}, {4656,5813}, {4847,5250}, {4857,10039}, {4915,12541}, {5048,10543}, {5173,12564}, {5223,6764}, {5225,9578}, {5252,9670}, {5289,12437}, {5290,9812}, {5698,6762}, {5703,11522}, {5704,9588}, {5722,11362}, {5759,6766}, {5919,6284}, {6666,9710}, {6700,8715}, {8162,10404}, {8390,12574}, {9669,10175}, {9799,9949}, {9804,9898}, {9845,12246}, {10165,11373}, {10172,10593}
X(12575) = midpoint of X(i) and X(j) for these {i,j}: {1,10624}, {145,12527}, {950,3057}, {6284,10106}
X(12575) = reflection of X(i) in X(j) for these (i,j): (65,6744), (4298,1), (6743,960)
X(12575) = X(389)-of-Hutson-intouch-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12576) lies on these lines: {20,8140}, {1125,8110}, {3244,11528}, {4292,11887}, {4297,8112}, {4298,8114}, {5935,12572}, {6744,11027}, {8108,12512}, {8386,12573}, {8392,12575}, {9837,12562}, {11686,12527}, {11855,12436}, {11857,12447}, {11893,12545}
X(12576) = reflection of X(12574) in X(20)
X(12576) = X(389)-of-outer-Hutson-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12577) lies on these lines: {1,7}, {4,9845}, {8,10980}, {10,1056}, {65,10569}, {85,10520}, {142,12513}, {226,3304}, {354,6738}, {388,9581}, {495,3634}, {496,12571}, {515,5045}, {518,11035}, {519,942}, {551,3487}, {553,3057}, {946,6259}, {950,5434}, {958,999}, {960,5850}, {1210,10827}, {1385,5763}, {1420,3475}, {3086,3947}, {3189,3244}, {3295,12512}, {3306,6736}, {3361,10164}, {3476,11518}, {3555,6743}, {3616,12527}, {3742,5795}, {3817,5290}, {3873,6737}, {4848,4860}, {4853,9776}, {4915,11024}, {5253,6745}, {5444,5563}, {5691,10580}, {5704,5726}, {5708,11362}, {5728,9850}, {7987,10578}, {10404,12053}, {11039,12574}, {11040,12576}
X(12577) = midpoint of X(i) and X(j) for these {i,j}: {1,4298}, {3555,6743}, {4292,12575}, {6738,10106}
X(12577) = reflection of X(6744) in X(5045)
X(12577) = X(389)-of-incircle-circles-triangle
X(12577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,7,4301), (1,3600,4297), (1,4292,12575), (1,4293,4314), (1,4295,4342), (1,4312,9785), (1,4317,4304), (1,4321,12520), (1,4355,962), (1,5542,12563), (1,11037,5542), (354,10106,6738), (1056,3333,10), (4298,12575,4292), (4308,11038,1)
The reciprocal orthologic center of these triangles is X(1).
X(12578) lies on these lines: {1,9789}, {3,142}, {10,8231}, {20,8244}, {515,12490}, {519,9808}, {3244,11532}, {3634,8230}, {4292,10885}, {4297,8234}, {4298,8243}, {6744,11030}, {8228,12571}, {8233,12572}, {8237,12573}, {8239,12575}, {10867,12447}, {10891,12545}, {11042,12577}, {11687,12527}, {11922,12574}
X(12578) = X(389)-of-2nd-Pamfilos-Zhou-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12579) lies on these lines: {1,6646}, {10,846}, {20,8245}, {21,36}, {405,3821}, {515,9959}, {516,9840}, {519,2292}, {1284,4298}, {2392,3884}, {3244,11533}, {3634,5051}, {3647,8258}, {4085,5302}, {4297,8235}, {4656,8669}, {6685,12572}, {6744,11031}, {8238,12573}, {8240,12575}, {11043,12577}, {11688,12527}
X(12579) = X(389)-of-1st-Sharygin-triangle
X(12579) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13246)
X(12579) = {X(21), X(4425)}-harmonic conjugate of X(1125)
The reciprocal orthologic center of these triangles is X(1).
X(12580) lies on these lines: {1,9793}, {10,8078}, {20,8089}, {515,8099}, {516,8091}, {519,8093}, {950,10503}, {1125,8077}, {2089,4298}, {3244,11534}, {3634,8087}, {4292,11888}, {4297,8081}, {6744,11032}, {10106,10506}
X(12580) = reflection of X(12581) in X(1)
X(12580) = X(389)-of-tangential-midarc-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12581) lies on these lines: {1,9793}, {10,258}, {20,8090}, {174,4298}, {515,8100}, {516,8092}, {519,8094}, {942,5571}, {950,10501}, {1125,7588}, {3244,11899}, {3634,8088}, {4292,11889}, {4297,8082}, {4355,11891}, {5542,7590}, {6744,11033}, {8423,11037}
X(12581) = reflection of X(12580) in X(1)
X(12581) = X(389)-of-2nd-tangential-midarc-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12582) lies on these lines: {1,11891}, {20,8423}, {174,4298}, {515,12491}, {519,12130}, {950,10502}, {1125,7587}, {3244,11535}, {3634,8382}, {6744,8083}, {8126,12527}, {8425,12579}, {8729,12436}, {11860,12447}, {11996,12578}
The reciprocal orthologic center of these triangles is X(3).
X(12583) lies on these lines: {6,402}, {30,599}, {69,4240}, {141,1650}, {159,11853}, {511,11251}, {518,12438}, {524,1651}, {611,11912}, {613,11913}, {1351,11911}, {1386,11831}, {1503,12113}, {1843,11832}, {2781,12369}, {3056,11909}, {3094,11885}, {3242,11910}, {3416,11900}, {3564,12418}, {3751,11852}, {5181,9033}, {5480,11897}, {6776,11845}, {9830,12347}, {11839,12212}, {11848,12329}, {11863,12452}
X(12583) = midpoint of X(69) and X(4240)
X(12583) = reflection of X(i) in X(j) for these (i,j): (6,402), (1650,141)
X(12583) = X(6)-of-Gossard-triangle
X(12583) = {X(11901),X(11902)}-harmonic conjugate of X(402)
The reciprocal orthologic center of these triangles is X(12585).
X(12584) lies on these lines: {3,67}, {6,11935}, {23,110}, {24,5095}, {54,575}, {74,12074}, {143,576}, {159,2777}, {182,1511}, {399,1350}, {524,7575}, {526,8723}, {597,11694}, {690,11616}, {1177,10282}, {1352,12383}, {1385,2836}, {1995,5476}, {2781,5609}, {2892,9833}, {3043,6403}, {3098,5663}, {5092,11579}, {5480,10272}, {5562,8718}, {5972,11284}, {7464,11645}, {7492,9143}, {7496,9140}, {7556,11061}, {9925,9932}, {10510,11649}
X(12584) = midpoint of X(i) and X(j) for these {i,j}: {3,2930}, {399,1350}, {1352,12383}, {2892,9833}
X(12584) = reflection of X(i) in X(j) for these (i,j): (182,1511), (576,6593), (597,11694), (895,575), (1177,10282), (5476,5642), (5480,10272), (9976,182), (11579,5092)
X(12584) = circumcircle-inverse-of-X(8724)
X(12584) = circummedial-to-1st-Ehrmann similarity image of X(14682)
The reciprocal orthologic center of these triangles is X(12584).
X(12585) lies on these lines: {6,5449}, {69,569}, {141,575}, {193,8538}, {389,3564}, {511,12370}, {524,1216}, {542,6102}, {1147,5181}, {2393,10116}
X(12585) = {X(141), X(575)}-harmonic conjugate of X(6689)
X(12585) = X(1156)-of-1st-Hyacinth-triangle if ABC is acute
X(12585) = orthic-to-1st-Hyacinth similarity image of X(5095)
The reciprocal orthologic center of these triangles is X(3).
X(12586) lies on these lines: {1,5820}, {4,8679}, {6,11}, {12,12594}, {66,1439}, {69,674}, {141,1376}, {159,10829}, {354,1899}, {355,518}, {375,7392}, {511,10525}, {524,11235}, {611,10523}, {613,10948}, {1350,11826}, {1351,11928}, {1386,11373}, {1503,12114}, {1709,7289}, {1843,11390}, {2781,12371}, {2810,3818}, {3056,10947}, {3094,10871}, {3242,10944}, {3410,4430}, {3416,10914}, {3564,10943}, {3618,10584}, {3751,10826}, {3873,11442}, {5480,10893}, {5810,10916}, {5846,10912}, {5927,9004}, {6776,10785}, {7595,9043}, {9018,10446}, {9830,12348}, {10794,12212}, {10945,12590}, {10946,12591}, {10949,12595}, {11865,12452}, {11866,12453}, {11903,12583}
X(12586) = reflection of X(i) in X(j) for these (i,j): (12329,141), (12587,1352)
X(12586) = X(6)-of-inner-Johnson-triangle
X(12586) = Ursa-minor-to-Ursa-major similarity image of X(6)
X(12586) = {X(10919),X(10920)}-harmonic conjugate of X(11)
X(12586) = {X(12928),X(12929)}-harmonic conjugate of X(10943)
The reciprocal orthologic center of these triangles is X(3).
X(12587) lies on these lines: {4,674}, {6,12}, {10,9028}, {11,12595}, {66,72}, {69,313}, {141,958}, {159,10830}, {210,1899}, {355,518}, {375,11433}, {498,5135}, {511,10526}, {524,11236}, {611,10954}, {613,10523}, {1350,11827}, {1351,11929}, {1386,11374}, {1478,4259}, {1503,11500}, {1843,11391}, {2321,2385}, {2781,12372}, {3056,10953}, {3094,10872}, {3242,10950}, {3410,4661}, {3618,10585}, {3681,11442}, {3751,5820}, {3818,9052}, {3844,5791}, {5220,5845}, {5480,10894}, {5810,5847}, {6776,10786}, {9830,12349}, {10795,12212}, {10951,12590}, {10952,12591}, {10955,12594}, {11867,12452}, {11868,12453}, {11904,12583}
X(12587) = reflection of X(12586) in X(1352)
X(12587) = X(6)-of-outer-Johnson-triangle
X(12587) = {X(10921),X(10922)}-harmonic conjugate of X(12)
X(12587) = {X(12938),X(12939)}-harmonic conjugate of X(10942)
The reciprocal orthologic center of these triangles is X(3).
X(12588) lies on these lines: {1,1352}, {2,1428}, {4,3056}, {5,613}, {6,12}, {7,8}, {11,10516}, {55,1503}, {56,141}, {66,73}, {67,3028}, {159,10831}, {182,498}, {193,5261}, {226,4362}, {495,611}, {511,1478}, {524,11237}, {542,10053}, {599,5434}, {612,1899}, {1330,1431}, {1350,7354}, {1351,9654}, {1386,11375}, {1460,11358}, {1479,3818}, {1843,11392}, {2099,5846}, {2330,3085}, {2781,12373}, {3027,11646}, {3094,9597}, {3098,4299}, {3242,10944}, {3600,3620}, {3618,10588}, {3619,7288}, {3745,5712}, {3751,9578}, {3763,5433}, {3961,5018}, {4260,9552}, {4293,10519}, {5052,9650}, {5085,5432}, {5480,10895}, {5848,10956}, {6284,10387}, {8540,10590}, {9830,12350}, {10072,11178}, {10797,12212}, {10957,12595}, {11501,12329}, {11869,12452}, {11870,12453}, {11905,12583}, {11930,12590}, {11931,12591}
X(12588) = reflection of X(611) in X(495)
X(12588) = X(6)-of-1st-Johnson-Yff-triangle
X(12588) = outer-Johnson-to-ABC similarity image of X(6)
X(12588) = {X(10923),X(10924)}-harmonic conjugate of X(12)
X(12588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1352,12589), (69,388,1469), (3085,6776,2330), (12941,12942,10056)
The reciprocal orthologic center of these triangles is X(3).
X(12589) lies on these lines: {1,1352}, {2,2330}, {4,1469}, {5,611}, {6,11}, {7,4459}, {12,10516}, {55,141}, {56,1503}, {69,350}, {159,10832}, {182,499}, {193,5274}, {354,5738}, {390,3620}, {496,613}, {511,1479}, {518,1837}, {524,11238}, {542,10069}, {599,3058}, {614,1899}, {1350,6284}, {1351,9669}, {1386,5820}, {1428,3086}, {1478,3818}, {1843,11393}, {2098,5846}, {2781,12374}, {2892,10118}, {3023,11646}, {3057,3416}, {3094,9598}, {3098,4302}, {3242,10950}, {3486,5484}, {3582,11179}, {3618,10589}, {3619,5218}, {3751,9581}, {3763,5432}, {4260,9555}, {4294,10519}, {5052,9665}, {5085,5433}, {5480,10896}, {5596,10535}, {5716,10372}, {5847,12053}, {5849,10959}, {7191,11442}, {7194,7281}, {9830,12351}, {10056,11178}, {10798,12212}, {10958,12594}, {11502,12329}, {11871,12452}, {11872,12453}, {11906,12583}, {11932,12590}, {11933,12591}
X(12589) = reflection of X(613) in X(496)
X(12589) = X(6)-of-2nd-Johnson-Yff-triangle
X(12589) = inner-Johnson-to-ABC similarity image of X(6)
X(12589) = {X(10925),X(10926)}-harmonic conjugate of X(11)
X(12589) = Ursa-major-to-Ursa-minor similarity image of X(6)
X(12589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1352,12588), (69,497,3056), (3086,6776,1428), (12951,12952,10072)
The reciprocal orthologic center of these triangles is X(3).
X(12590) lies on these lines: {6,493}, {69,6462}, {141,8222}, {159,8194}, {511,10669}, {518,12440}, {524,12152}, {611,11951}, {613,11953}, {1350,11828}, {1351,11949}, {1352,8220}, {1386,11377}, {1503,9838}, {1843,11394}, {2781,12377}, {3056,11947}, {3094,10875}, {3242,8210}, {3416,8214}, {3564,12426}, {3751,8188}, {5013,6461}, {5480,8212}, {6776,11846}, {8201,12452}, {8208,12453}, {9830,12352}, {10945,12586}, {10951,12587}, {11503,12329}, {11840,12212}, {11907,12583}, {11930,12588}, {11932,12589}, {11955,12594}, {11957,12595}
X(12590) = X(6)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12591) lies on these lines: {6,494}, {69,6463}, {141,8223}, {159,8195}, {511,10673}, {518,12441}, {524,12153}, {611,11952}, {613,11954}, {1350,11829}, {1351,11950}, {1352,8221}, {1386,11378}, {1503,9839}, {1843,11395}, {2781,12378}, {3056,11948}, {3094,10876}, {3242,8211}, {3416,8215}, {3564,12427}, {3751,8189}, {5013,6461}, {5480,8213}, {6776,11847}, {8202,12452}, {8209,12453}, {9830,12353}, {10946,12586}, {10952,12587}, {11504,12329}, {11841,12212}, {11908,12583}, {11931,12588}, {11933,12589}, {11956,12594}, {11958,12595}
X(12591) = X(6)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(3779).
X(12592) lies on these lines: {}
The reciprocal orthologic center of these triangles is X(6).
X(12593) lies on the line {576,2781}
The reciprocal orthologic center of these triangles is X(3).
X(12594) lies on these lines: {1,6}, {12,12586}, {55,8679}, {69,10528}, {119,10516}, {141,5552}, {159,10834}, {221,5252}, {495,5820}, {511,10679}, {524,11239}, {1350,11248}, {1351,12000}, {1352,10942}, {1469,11509}, {1470,5096}, {1503,12115}, {1843,11400}, {2097,3359}, {2781,12381}, {3056,10965}, {3094,10878}, {3416,10915}, {3564,12430}, {3618,10586}, {5085,10269}, {5480,10531}, {5848,10956}, {6776,10805}, {9830,12356}, {10803,12212}, {10955,12587}, {10958,12589}, {11881,12452}, {11882,12453}, {11914,12583}, {11955,12590}, {11956,12591}
X(12594) = reflection of X(i) in X(j) for these (i,j): (6,611), (5820,495)
X(12594) = X(6)-of-inner-Yff-tangents-triangle
X(12594) = outer-Yff-to-inner-Yff similarity image of X(6)
X(12594) = {X(10929),X(10930)}-harmonic conjugate of X(1)
X(12594) = {X(6), X(3242)}-harmonic conjugate of X(12595)
The reciprocal orthologic center of these triangles is X(3).
X(12595) lies on these lines: {1,6}, {11,12587}, {56,674}, {69,10529}, {141,10527}, {159,10835}, {511,10680}, {524,11240}, {999,4259}, {1350,11249}, {1351,12001}, {1352,10943}, {1428,11510}, {1503,12116}, {1843,11401}, {3056,10966}, {3094,10879}, {3295,5135}, {3416,10916}, {3564,12431}, {3618,10587}, {4265,10387}, {5085,10267}, {5480,10532}, {5849,10959}, {6776,10806}, {9028,12053}, {9830,12357}, {10804,12212}, {10949,12586}, {10957,12588}, {11883,12452}, {11915,12583}, {11957,12590}, {11958,12591}
X(12595) = reflection of X(6) in X(613)
X(12595) = X(6)-of-outer-Yff-tangents-triangle
X(12595) = inner-Yff-to-outer-Yff similarity image of X(6)
X(12595) = {X(10931),X(10932)}-harmonic conjugate of X(1)
X(12595) = {X(6), X(3242)}-harmonic conjugate of X(12594)
The reciprocal orthologic center of these triangles is X(10112).
X(12596) lies on these lines: {6,1511}, {74,11416}, {110,8537}, {113,8541}, {125,8538}, {265,895}, {1351,1986}, {1539,9970}, {1992,12319}, {5663,8549}, {6699,11511}, {11405,12168}, {11443,12273}, {11458,12284}, {11470,12295}, {11477,12302}, {11482,12310}
X(12596) = midpoint of X(11477) and X(12302)
The reciprocal orthologic center of these triangles is X(3).
X(12597) lies on these lines: {6,12229}, {486,11511}, {487,8541}, {642,9813}, {1992,12320}, {3564,12598}, {8537,12509}, {8538,12601}, {11405,12169}, {11416,12221}, {11443,12274}, {11458,12285}, {11470,12296}, {11477,12303}, {11482,12311}
X(12597) = orthic-to-2nd-Ehrmann similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12598) lies on these lines: {6,12230}, {485,11511}, {488,8541}, {641,9813}, {1992,12321}, {3564,12597}, {8537,12510}, {8538,12602}, {11405,12170}, {11416,12222}, {11443,12275}, {11458,12286}, {11470,12297}, {11477,12304}, {11482,12312}
X(12598) = orthic-to-2nd-Ehrmann similarity image of X(488)
The reciprocal orthologic center of these triangles is X(40).
X(12599) lies on these lines: {2,12120}, {4,1697}, {10,5805}, {98,12200}, {235,12139}, {515,12260}, {946,10157}, {1478,10075}, {1479,10059}, {1598,12411}, {1699,9898}, {3091,9874}, {3851,12620}, {4866,7682}, {5290,7992}, {5534,12521}, {5603,8000}, {6245,7680}, {6841,12612}, {8196,12464}, {8203,12465}, {9993,12500}, {11496,12333}
X(12599) = midpoint of X(4) and X(7160)
X(12599) = complement of X(12120)
X(12599) = X(7160)-of-Euler-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12600) lies on these lines: {4,5885}, {11,79}, {98,12209}, {235,12146}, {515,12267}, {1598,12414}, {1699,12409}, {6265,6599}, {6841,12615}, {8196,12482}, {8203,12483}, {9993,12504}, {11496,12342}
X(12600) = midpoint of X(4) and X(10266)
X(12600) = X(10266)-of-Euler-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12601) lies on these lines: {2,12509}, {3,486}, {4,193}, {5,487}, {30,12256}, {52,12237}, {355,7596}, {381,1991}, {494,8036}, {517,9906}, {569,12229}, {642,1656}, {999,10083}, {1587,11482}, {1588,5050}, {1598,12147}, {3070,5093}, {3295,10067}, {3526,6119}, {3830,6280}, {3843,6281}, {5139,8946}, {5446,6291}, {6565,9732}, {6643,12320}, {7395,12169}, {7517,9921}, {7980,10247}, {8538,12597}, {9301,9986}, {10246,12268}, {11444,12274}, {11459,12285}, {11842,12210}, {11849,12343}, {11875,12484}, {11876,12485}
X(12601) = midpoint of X(i) and X(j) for these {i,j}: {4,12221}, {12256,12296}
X(12601) = reflection of X(i) in X(j) for these (i,j): (3,486), (52,12237), (487,5), (6290,6251)
X(12601) = complement of X(12509)
X(12601) = orthic-to-2nd-Euler similarity image of X(487)
X(12601) = {X(4),X(1351)}-harmonic conjugate of X(12602)
The reciprocal orthologic center of these triangles is X(3).
X(12602) lies on these lines: {2,12510}, {3,485}, {4,193}, {5,488}, {30,12257}, {52,12238}, {493,8035}, {517,9907}, {569,12230}, {641,1656}, {999,10084}, {1587,5050}, {1588,11482}, {1598,12148}, {3071,5093}, {3295,10068}, {3526,6118}, {3830,6279}, {3843,6278}, {5139,8948}, {5200,8780}, {5446,6406}, {6564,9733}, {6643,12321}, {7395,12170}, {7517,9922}, {7981,10247}, {8538,12598}, {8982,10846}, {9301,9987}, {10246,12269}, {11444,12275}, {11459,12286}, {11842,12211}, {11849,12344}, {11875,12486}, {11876,12487}
X(12602) = midpoint of X(i) and X(j) for these {i,j}: {4,12222}, {12257,12297}
X(12602) = reflection of X(i) in X(j) for these (i,j): (3,485), (52,12238), (488,5), (6289,6250)
X(12602) = complement of X(12510)
X(12602) = orthic-to-2nd-Euler similarity image of X(488)
X(12602) = {X(4),X(1351)}-harmonic conjugate of X(12601)
The reciprocal orthologic center of these triangles is X(3).
X(12603) lies on these lines: {2,6239}, {3,6}, {4,12223}, {5,6291}, {30,12298}, {487,1216}, {1060,7362}, {1062,6283}, {1656,9823}, {6252,8251}, {6413,10670}, {6643,12322}, {7395,12171}, {11444,12276}, {11459,12287}
X(12603) = midpoint of X(4) and X(12223)
X(12603) = reflection of X(i) in X(j) for these (i,j): (3,12360), (52,12239), (6291,5)
X(12603) = complement of X(6239)
X(12603) = X(176)-of-2nd-Euler-triangle if ABC is acute
X(12603) = orthic-to-2nd-Euler similarity image of X(6291)
X(12603) = {X(3),X(9967)}-harmonic conjugate of X(12604)
The reciprocal orthologic center of these triangles is X(3).
X(12604) lies on these lines: {2,6400}, {3,6}, {4,12224}, {5,6406}, {30,12299}, {51,8964}, {488,1216}, {1060,7353}, {1062,6405}, {1656,9824}, {6404,8251}, {6414,10674}, {6643,12323}, {7395,12172}, {11444,12277}, {11459,12288}
X(12604) = midpoint of X(4) and X(12224)
X(12604) = reflection of X(i) in X(j) for these (i,j): (3,12361), (52,12240), (6406,5)
X(12604) = complement of X(6400)
X(12604) = X(175)-of-2nd-Euler-triangle if ABC is acute
X(12604) = orthic-to-2nd-Euler similarity image of X(6406)
X(12604) = {X(3),X(9967)}-harmonic conjugate of X(12603)
The reciprocal orthologic center of these triangles is X(4).
X(12605) lies on these lines: {2,3}, {52,12241}, {68,4549}, {131,10600}, {216,7747}, {339,7767}, {343,9927}, {394,12118}, {569,12233}, {577,7748}, {973,5446}, {1038,10483}, {1060,7354}, {1062,6284}, {1154,12370}, {1176,3521}, {1216,12358}, {1503,9967}, {1568,9820}, {1899,12163}, {3070,10897}, {3071,10898}, {3284,7765}, {5254,10316}, {5305,10317}, {5318,10634}, {5321,10635}, {5596,12315}, {5889,12022}, {5907,12134}, {6102,11245}, {6146,10116}, {6253,8251}, {7723,12606}, {8538,8550}, {11064,12038}, {11444,12278}, {11459,12289}
X(12605) = midpoint of X(i) and X(j) for these {i,j}: {4,12225}, {11750,12162}
X(12605) = reflection of X(i) in X(j) for these (i,j): (3,12362), (52,12241), (3575,5), (7553,4), (11819,546), (12134,5907)
X(12605) = complement of X(6240)
X(12605) = anticomplement of X(31833)
X(12605) = X(65)-of-2nd-Euler-triangle if ABC is acute
X(12605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,7547,5), (3,5,7542), (3,381,3549), (3,2072,140), (3,10024,6676), (3,11585,10257), (4,20,7387), (4,3529,7500), (4,5133,546), (4,7404,381), (4,7503,5), (4,7566,3845), (5,550,1658), (5,1658,468), (381,3534,10245), (381,9714,3089), (546,6676,10024), (546,11819,428), (1556,6656,546), (3091,7569,5), (7542,10297,5)
The reciprocal orthologic center of these triangles is X(6243).
X(12606) lies on these lines: {2,6242}, {3,54}, {4,12226}, {5,6152}, {30,12300}, {52,12242}, {68,3519}, {125,1216}, {381,11576}, {539,5562}, {569,12234}, {973,6639}, {1060,7356}, {1062,6286}, {1209,2072}, {1352,6288}, {1656,9827}, {2914,7512}, {3574,5446}, {4549,9936}, {5876,12289}, {5965,9967}, {6255,8251}, {6643,12325}, {7395,12175}, {7542,8254}, {7723,12605}, {8538,9977}, {10634,10677}, {10635,10678}, {11444,12280}, {11459,12291}
X(12606) = midpoint of X(4) and X(12226)
X(12606) = reflection of X(i) in X(j) for these (i,j): (3,12363), (52,12242), (6152,5)
X(12606) = X(79)-of-2nd-Euler-triangle if ABC is acute
X(12606) = complement of X(6242)
The reciprocal orthologic center of these triangles is X(1).
X(12607) lies on these lines: {1,1329}, {2,3304}, {3,529}, {4,528}, {5,519}, {8,12}, {10,141}, {11,145}, {20,4421}, {30,8715}, {55,3436}, {56,3035}, {65,6735}, {72,10039}, {78,5252}, {100,7354}, {119,1482}, {120,6552}, {140,8666}, {200,5794}, {226,5836}, {341,3932}, {355,3811}, {377,11237}, {388,1376}, {404,5434}, {405,10056}, {442,3679}, {452,4428}, {496,3244}, {498,956}, {517,10915}, {535,550}, {631,11194}, {758,5499}, {908,3057}, {938,5828}, {946,3880}, {958,3085}, {976,5724}, {999,6691}, {1001,2551}, {1125,3820}, {1210,5123}, {1215,5835}, {1259,11501}, {1478,5687}, {1532,7982}, {1698,6762}, {1699,2136}, {1706,5290}, {1737,3555}, {1837,3870}, {1904,3175}, {2098,10958}, {2478,3303}, {2550,5261}, {2802,11698}, {2829,11248}, {2975,5432}, {3036,10573}, {3058,5046}, {3086,6667}, {3091,11235}, {3158,5691}, {3241,4193}, {3419,10827}, {3428,10786}, {3434,10895}, {3584,5258}, {3614,3621}, {3617,3925}, {3625,10592}, {3626,3822}, {3632,7951}, {3633,7741}, {3635,3825}, {3671,10107}, {3680,11522}, {3698,5249}, {3703,4696}, {3704,4385}, {3742,8582}, {3746,11113}, {3754,6147}, {3782,4642}, {3838,3947}, {3841,4691}, {3871,5080}, {3928,9588}, {3935,5086}, {3991,5179}, {4004,11551}, {4030,5016}, {4188,6174}, {4189,4995}, {4190,9657}, {4423,10587}, {4511,10944}, {4640,12527}, {4853,5219}, {4882,5726}, {4930,6980}, {5082,8168}, {5087,12053}, {5176,10950}, {5187,11238}, {5220,5815}, {5270,11112}, {5587,6765}, {5603,10912}, {5657,5852}, {5718,10459}, {5734,6945}, {5842,10526}, {5881,6831}, {5882,6922}, {6067,7679}, {6256,10306}, {6675,10197}, {6692,12577}, {6745,10106}, {6764,7958}, {6869,11500}, {6907,11362}, {6931,11240}, {7373,10200}, {7988,11519}, {8668,11496}, {8727,12437}, {9565,10408}, {9708,10198}, {9712,10037}, {9713,10831}, {9779,12541}, {9947,12617}, {9956,10916}, {10310,12115}, {10863,12448}, {10883,12536}, {10886,12546}, {10914,12047}, {11491,11827}
X(12607) = midpoint of X(i) and X(j) for these {i,j}: {4,3913}, {355,3811}, {6256,10306}
X(12607) = reflection of X(i) in X(j) for these (i,j): (3813,5), (8666,140), (10916,9956), (11260,1125)
X(12607) = complement of X(12513)
X(12607) = X(64)-of-3rd-Euler-triangle
X(12607) = excentral-to-3rd-Euler similarity image of X(2136)
X(12607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1329,3816), (5,3813,3829), (8,12,2886), (56,5552,3035), (65,6735,8256), (119,1482,7681), (145,11681,11), (200,9578,5794), (226,6736,5836), (388,7080,1376), (442,3679,9710), (498,956,4999), (958,3085,6690), (1706,5290,5880), (2478,11239,3303), (3085,3421,958), (3244,3814,496), (3436,10528,55), (3584,5258,7483), (3913,11236,4)
The reciprocal orthologic center of these triangles is X(72).
Let Na be the nine-point center of BCI, and define Nb and Nc cyclically. Triangle NaNbNc is perspective to the 3rd Euler triangle at X(12608). (Randy Hutson, July 21, 2017)
X(12608) lies on these lines: {1,4}, {2,1158}, {5,3812}, {10,119}, {21,10165}, {40,908}, {46,6834}, {65,1532}, {84,5249}, {90,499}, {142,3358}, {153,4861}, {411,2077}, {516,6796}, {517,10915}, {912,10916}, {920,3911}, {942,1538}, {960,6907}, {962,10528}, {971,9955}, {997,6850}, {1012,11375}, {1125,3560}, {1210,1858}, {1385,2829}, {1470,4292}, {1537,3057}, {1709,6833}, {1737,6941}, {1770,6905}, {1788,6969}, {1836,3149}, {2096,7288}, {2360,3559}, {2476,7705}, {2886,5777}, {2950,5316}, {3359,3452}, {3474,6927}, {3576,6872}, {3612,6938}, {3657,6003}, {3671,7682}, {3816,9940}, {3817,6245}, {3869,6735}, {4295,6848}, {4297,7491}, {5086,12531}, {5087,6922}, {5119,10786}, {5261,10935}, {5440,11826}, {5554,5587}, {5693,6734}, {5698,6988}, {5722,10893}, {5768,10591}, {5880,6918}, {5886,6259}, {5905,10530}, {6147,7956}, {6247,6708}, {6827,12520}, {6828,9948}, {6856,10172}, {6867,9842}, {6943,9961}, {6968,10826}, {7680,9856}, {7988,7992}, {8085,8095}, {8086,8096}, {8727,9942}, {9779,9799}, {9960,10883}, {10085,10785}, {10679,11500}, {10724,11015}, {10886,12547}, {11019,12005}, {11372,11919}, {11374,11496}, {11680,12528}
X(12608) = midpoint of X(i) and X(j) for these {i,j}: {1,6256}, {4,6261}, {946,6260}, {6259,12114}
X(12608) = reflection of X(i) in X(j) for these (i,j): (5450,1125), (10915,10942), (12616,5)
X(12608) = complement of X(1158)
X(12608) = X(68)-of-3rd-Euler-triangle
X(12608) = excentral-to-3rd-Euler similarity image of X(1490)
X(12608) = 3rd-Euler-isotomic conjugate of X(12610)
X(12608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1519,946), (1,1699,10531), (4,12047,946), (942,1538,7681), (946,5882,12053), (5087,9943,6922), (5603,10805,1), (5886,6259,12114), (5887,6842,10), (6825,12514,6684), (6838,11415,40)
The reciprocal orthologic center of these triangles is X(65).
Let (Oa), (Ob), (Oc) be the Odehnal tritangent circles. Let La be the polar of A wrt (Oa), and define Lb, Lc cyclically. La is also the line through the touchpoints of (Oa) and CA and AB, and cyclically for Lb and Lc. Let A' = Lb∩Lc, B' = Lc∩La, C' = La∩Lb. Triangle A'B'C' is homothetic to the extraversion triangle of X(10) at X(12609). (Randy Hutson, July 21, 2017)
X(12609) lies on these lines: {1,224}, {2,46}, {3,142}, {4,12520}, {5,3812}, {8,12559}, {10,12}, {11,5439}, {21,1770}, {40,6889}, {79,5251}, {191,11552}, {306,4647}, {386,1738}, {405,1836}, {443,997}, {474,11375}, {495,5836}, {496,3742}, {499,3306}, {515,6917}, {517,3824}, {518,6147}, {519,5794}, {551,2646}, {908,1698}, {936,12560}, {942,2886}, {956,10404}, {960,8728}, {993,4292}, {1004,10624}, {1089,4054}, {1155,6681}, {1158,6824}, {1159,3626}, {1210,5883}, {1213,4047}, {1376,11374}, {1385,5842}, {1454,3911}, {1519,5437}, {1699,6836}, {1709,6837}, {1737,2476}, {1788,6856}, {1858,10395}, {2245,5257}, {2475,10572}, {2550,3487}, {2551,5714}, {3011,5264}, {3086,9776}, {3159,4078}, {3333,6173}, {3338,10044}, {3339,5705}, {3452,3634}, {3474,6857}, {3475,5082}, {3556,7535}, {3576,6934}, {3579,6690}, {3612,3616}, {3624,4512}, {3772,5711}, {3813,5045}, {3814,8582}, {3816,9955}, {3817,3825}, {3826,5044}, {3827,9895}, {3868,11551}, {3869,4197}, {3874,4847}, {3881,5542}, {3884,4301}, {3916,11246}, {4298,8666}, {4324,5426}, {4425,12567}, {4640,6675}, {5047,5057}, {5086,6175}, {5123,10592}, {5226,11024}, {5290,9623}, {5302,11544}, {5554,10827}, {5587,6984}, {5603,6897}, {5690,10107}, {5887,6881}, {5902,6734}, {6261,6826}, {6667,12611}, {6668,11231}, {6691,11230}, {6692,6862}, {6860,7988}, {6871,10826}, {6887,8257}, {6907,7686}, {6955,9624}, {8727,9943}, {9614,10582}, {9779,9800}, {9949,10863}, {9961,10883}, {10478,12544}, {10886,12548}, {11019,12446}, {11680,12529}
X(12609) = midpoint of X(i) and X(j) for these {i,j}: {4,12520}, {8,12559}, {10,3671}, {4295,12514}, {12446,12564}
X(12609) = reflection of X(i) in X(j) for these (i,j): (10,3841), (5248,1125), (12617,5)
X(12609) = complement of X(12514)
X(12609) = excentral-to-3rd-Euler similarity image of X(12565)
X(12609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,4295,12514), (10,3919,4848), (10,4138,3454), (10,11263,226), (12,3753,10), (65,442,10), (72,3925,10), (142,946,1125), (443,3485,997), (495,5836,10915), (942,2886,10916), (2550,3487,3811), (3616,4190,3612), (3649,3925,72), (3754,3822,10), (3754,6701,3822), (3812,3838,5), (3817,9843,3825), (3825,3833,9843), (5437,8227,10200)
The reciprocal orthologic center of these triangles is X(65).
X(12610) lies on these lines: {2,1766}, {3,142}, {4,990}, {5,3739}, {8,11532}, {10,8230}, {57,1848}, {75,7377}, {116,2823}, {141,517}, {226,1465}, {355,4361}, {497,10383}, {515,3946}, {573,4357}, {908,3729}, {942,5799}, {952,4852}, {971,5480}, {1418,1565}, {1482,4851}, {1699,1721}, {1826,4858}, {1890,3220}, {2050,3772}, {2345,7402}, {3662,10446}, {3817,8228}, {4104,10440}, {4353,11042}, {4384,5816}, {4425,8246}, {4648,5603}, {5249,10444}, {5393,7133}, {5405,7595}, {6003,10099}, {6245,7683}, {6707,11230}, {7988,7996}, {8239,12053}, {8727,9944}, {9779,9801}, {9950,10863}, {9962,10883}, {10867,11019}, {10886,12549}, {11680,12530}
X(12610) = midpoint of X(i) and X(j) for these {i,j}: {4,990}, {3663,10445}
X(12610) = reflection of X(12618) in X(5)
X(12610) = complement of X(1766)
X(12610) = X(317)-of-3rd-Euler-triangle
X(12610) = excentral-to-3rd-Euler similarity image of X(1721)
X(12610) = 3rd-Euler-isotomic conjugate of X(12608)
The reciprocal orthologic center of these triangles is X(3869).
X(12611) lies on these lines: {1,10742}, {2,12515}, {4,6224}, {5,2800}, {11,113}, {30,214}, {80,381}, {104,5886}, {119,517}, {142,6713}, {153,5603}, {226,1387}, {355,10698}, {382,12119}, {496,5083}, {546,946}, {1320,3656}, {1385,2829}, {1484,2801}, {1699,6326}, {1768,8227}, {1836,10090}, {2802,11698}, {3035,3579}, {3091,12247}, {3616,12248}, {3817,10265}, {4996,5057}, {5316,11231}, {5660,12331}, {5840,9945}, {5854,11278}, {5901,11715}, {6264,11522}, {6667,12609}, {6911,12332}, {7704,12528}, {8727,9946}, {9779,9803}, {9818,9912}, {9952,10863}, {9957,10956}, {9964,10883}, {10057,10895}, {10058,11375}, {10073,10896}, {10074,11376}, {10284,10942}, {10886,12551}, {11680,12532}
X(12611) = midpoint of X(i) and X(j) for these {i,j}: {1,10742}, {4,6265}, {119,1537}, {355,10698}, {382,12119}, {3656,10711}, {6326,10738}
X(12611) = reflection of X(i) in X(j) for these (i,j): (11,9955), (1385,11729), (3579,3035), (11715,5901), (12619,5)
X(12611) = complement of X(12515)
X(12611) = X(265)-of-3rd-Euler-triangle
X(12611) = X(12121)-of-4th-Euler-triangle
X(12611) = excentral-to-3rd-Euler similarity image of X(6326)
X(12611) = {X(1699), X(6326)}-harmonic conjugate of X(10738)
The reciprocal orthologic center of these triangles is X(3555).
X(12612) lies on these lines: {2,12516}, {4,12521}, {5,4662}, {12,5920}, {142,5709}, {226,9589}, {946,6765}, {6838,7160}, {6841,12599}, {7988,8001}, {8727,12439}, {9779,9804}, {9953,10863}, {10883,12537}, {10886,12552}, {11680,12533}
X(12612) = midpoint of X(4) and X(12521)
X(12612) = reflection of X(12620) in X(5)
X(12612) = complement of X(12516)
The reciprocal orthologic center of these triangles is X(3555).
X(12613) lies on these lines: {2,12517}, {4,12522}, {5,12621}, {3825,6684}, {8727,12442}, {9779,12542}, {10863,12449}, {10883,12538}, {10886,12553}, {11680,12534}
X(12613) = midpoint of X(4) and X(12522)
X(12613) = reflection of X(12621) in X(5)
X(12613) = complement of X(12517)
The reciprocal orthologic center of these triangles is X(1).
X(12614) lies on these lines: {1,8085}, {5,12622}, {11,177}, {12,8422}, {164,1699}, {167,7988}, {226,5571}, {3679,8381}, {7670,7678}, {9779,9807}, {11680,11691}
X(12614) = midpoint of X(4) and X(12523)
X(12614) = reflection of X(12622) in X(5)
X(12614) = complement of X(12518)
X(12614) = X(1)-of-3rd-Euler-triangle
The reciprocal orthologic center of these triangles is X(21).
X(12615) lies on these lines: {2,12519}, {4,12524}, {5,12623}, {6841,12600}, {6949,12342}, {8727,12444}, {9779,12543}, {10863,12451}, {10883,12540}, {10886,12557}, {11680,12535}
X(12615) = midpoint of X(4) and X(12524)
X(12615) = reflection of X(12623) in X(5)
X(12615) = complement of X(12519)
The reciprocal orthologic center of these triangles is X(72).
Let (Oa), (Ob), (Oc) be the Odehnal tritangent circles. Let La be the polar of A wrt (Oa), and define Lb and Lc cyclically. La is also the line through the touchpoints of (Oa) and CA and AB, and cyclically for Lb, Lc. Let A' = Lb∩Lc, B' = Lc∩La, C' = La∩Lb. Let Ma be the polar of I wrt (Oa), and define Mb, Mc cyclically. Let A" = Mb∩Mc, B" = Mc∩Ma, C" = Ma∩Mb. Triangles A'B'C' and A"B"C" are homothetic at X(12616). (Randy Hutson, July 21, 2017)
Let A'B'C' be the excentral triangle. X(12616) is the radical center of the 1st Droz-Farny circles of triangles A'BC, B'CA, C'AB. (Randy Hutson, June 27, 2018)
X(12616) lies on these lines: {1,6833}, {2,6261}, {3,10}, {4,46}, {5,3812}, {8,6890}, {11,65}, {40,3434}, {63,10522}, {84,377}, {104,10057}, {224,5552}, {225,1735}, {226,5884}, {442,5927}, {516,10525}, {517,3813}, {581,5530}, {908,5693}, {942,7680}, {944,3612}, {950,11507}, {952,10915}, {960,6922}, {971,3826}, {997,6891}, {1012,1837}, {1072,3670}, {1125,6862}, {1329,5777}, {1385,6690}, {1454,4292}, {1490,1698}, {1512,4316}, {1519,7741}, {1699,10598}, {1715,1869}, {1765,1826}, {1768,3585}, {1771,3215}, {1777,1877}, {1898,10958}, {2096,5229}, {2245,10445}, {2646,5882}, {2829,12619}, {3057,10949}, {3085,5768}, {3338,10532}, {3339,5715}, {3419,10310}, {3485,6956}, {3486,6935}, {3576,6910}, {3579,5842}, {3869,6943}, {3916,11827}, {4197,9960}, {4295,6844}, {4511,6972}, {4847,10914}, {5086,6909}, {5119,12116}, {5563,11219}, {5657,6899}, {5722,11496}, {5761,12559}, {5818,6897}, {5881,6735}, {5887,6882}, {5905,10524}, {6825,12520}, {6827,12514}, {6830,12047}, {6860,7971}, {6906,10572}, {6907,9943}, {6913,12330}, {6932,9961}, {6984,7989}, {7483,10165}, {7681,9856}, {7682,10893}, {7686,8727}, {8087,8095}, {8088,8096}, {9780,9799}, {10044,10599}, {10085,10827}, {10624,10947}, {10887,12547}, {10948,12053}, {11019,11373}, {11681,12528}
X(12616) = midpoint of X(i) and X(j) for these {i,j}: {4,1158}, {10,6245}, {84,6256}, {355,12114}, {5787,11500}, {6260,9948}
X(12616) = reflection of X(i) in X(j) for these (i,j): (5450,6705), (6796,6684), (12608,5)
X(12616) = complement of X(6261)
X(12616) = X(68)-of-4th-Euler-triangle
X(12616) = excentral-to-4th-Euler similarity image of X(1490)
X(12616) = 4th-Euler-isotomic conjugate of X(12618)
X(12616) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (65,6831,946), (84,5587,6256), (944,6977,3612), (946,10265,1210), (1709,10826,4), (9948,10175,6260), (10085,10827,12115)
The reciprocal orthologic center of these triangles is X(65).
X(12617) lies on these lines: {1,6837}, {2,12520}, {4,9}, {5,3812}, {12,1898}, {21,4297}, {46,6835}, {65,8226}, {90,1478}, {118,5517}, {142,9948}, {226,1858}, {355,3913}, {377,1709}, {411,10164}, {515,3560}, {758,946}, {920,4292}, {960,8727}, {997,6847}, {1001,5787}, {1125,6245}, {1158,6826}, {1210,3671}, {1329,10157}, {1490,10198}, {1698,6838}, {1699,6734}, {1737,3091}, {1770,6839}, {2476,8582}, {2801,12564}, {2886,9856}, {3485,11019}, {3486,10389}, {3612,6974}, {3634,6825}, {3746,4314}, {3822,6260}, {3841,6842}, {3869,4301}, {4197,9961}, {4294,10039}, {4512,5691}, {5086,6736}, {5439,7958}, {5603,12559}, {5777,7680}, {6678,12262}, {6684,6985}, {6855,9843}, {6866,7682}, {6869,12512}, {6871,7989}, {6957,10826}, {8728,9943}, {9780,9800}, {9947,12607}, {10394,10865}, {10479,12544}, {10887,12548}, {11681,12529}
X(12617) = midpoint of X(i) and X(j) for these {i,j}: {4,12514}, {355,11496}
X(12617) = reflection of X(i) in X(j) for these (i,j): (946,12558), (12511,6684), (12609,5)
X(12617) = complement of X(12520)
X(12617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5887,6841,946), (6261,6824,1125), (6828,12047,3817), (6870,11415,1699)
ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th EULER TO 5th EXTOUCH
X(12618) lies on these lines: {1,5807}, {2,990}, {4,9}, {5,3739}, {118,123}, {141,971}, {307,1210}, {321,4712}, {517,5480}, {726,10916}, {962,5772}, {991,3912}, {1041,4347}, {1211,5927}, {1698,1721}, {1754,5294}, {2298,4349}, {3332,5749}, {3454,6260}, {3677,4353}, {3729,6734}, {4197,9962}, {4220,10164}, {4363,5805}, {4643,5779}, {5016,6736}, {5051,8582}, {5101,7085}, {5743,10157}, {7989,7996}, {8728,9944}, {9780,9801}, {10444,10479}, {10887,12549}, {11681,12530}
X(12618) = midpoint of X(4) and X(1766)
X(12618) = reflection of X(12610) in X(5)
X(12618) = complement of X(990)
X(12618) = X(317)-of-4th-Euler-triangle
X(12618) = excentral-to-4th-Euler similarity image of X(1721)
X(12618) = 4th-Euler-isotomic conjugate of X(12616)
X(12618) = {X(9), X(1861)}-harmonic conjugate of X(10)
The reciprocal orthologic center of these triangles is X(3869).
X(12619) lies on these lines: {2,6265}, {3,80}, {4,12515}, {5,2800}, {10,140}, {11,517}, {12,5885}, {24,12137}, {40,10738}, {55,10073}, {56,10057}, {65,8068}, {100,1006}, {104,355}, {119,125}, {149,5657}, {153,5818}, {495,5083}, {496,10284}, {631,6224}, {912,5123}, {1145,6734}, {1210,1387}, {1317,10039}, {1329,5694}, {1484,2802}, {1537,9955}, {1698,6326}, {1768,5587}, {1788,10526}, {1837,10058}, {2080,12198}, {2801,3826}, {2829,12616}, {3057,5533}, {3560,12332}, {3576,9897}, {3579,5840}, {3653,10031}, {3654,10707}, {3679,6264}, {4197,9964}, {4413,5790}, {5221,11929}, {5252,10074}, {5428,6684}, {5444,7972}, {5499,12623}, {5854,10916}, {5886,10698}, {6642,9912}, {6667,11230}, {6958,10573}, {7583,8988}, {7951,11571}, {8256,10943}, {8582,9952}, {8728,9946}, {9780,9803}, {10267,12331}, {10887,12551}, {11681,12532}
X(12619) = midpoint of X(i) and X(j) for these {i,j}: {3,80}, {4,12515}, {10,10265}, {40,10738}, {104,355}, {1484,5690}, {1768,10742}, {3654,10707}, {5790,11219}, {6265,12247}
X(12619) = reflection of X(i) in X(j) for these (i,j): (5,6702), (119,9956), (214,140), (1385,6713), (1537,9955), (11570,5885), (11729,6667), (12611,5)
X(12619) = complement of X(6265)
X(12619) = K798i-isogonal conjugate of X(3)
X(12619) = X(265)-of-4th-Euler-triangle
X(12619) = X(12121)-of-3rd-Euler-triangle
X(12619) = excentral-to-4th-Euler similarity image of X(6326)
X(12619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,12247,6265), (1768,5587,10742), (6667,11729,11230)
The reciprocal orthologic center of these triangles is X(3555).
X(12620) lies on these lines: {2,12521}, {4,12516}, {5,4662}, {10,6767}, {11,3983}, {442,3555}, {497,10395}, {3826,10916}, {3851,12599}, {4197,12537}, {5187,9874}, {5220,5812}, {7989,8001}, {8582,9953}, {8728,12439}, {9780,9804}, {10887,12552}, {11681,12533}
X(12620) = midpoint of X(4) and X(12516)
X(12620) = reflection of X(12612) in X(5)
X(12620) = complement of X(12521)
The reciprocal orthologic center of these triangles is X(3555).
X(12621) lies on these lines: {2,12522}, {4,12517}, {5,12613}, {4197,12538}, {5521,5687}, {8582,12449}, {8728,12442}, {9780,12542}, {10887,12553}, {11681,12534}
X(12621) = midpoint of X(4) and X(12517)
X(12621) = reflection of X(12613) in X(5)
X(12621) = complement of X(12522)
The reciprocal orthologic center of these triangles is X(1).
X(12622) lies on these lines: {1,8087}, {2,12523}, {4,12518}, {5,12614}, {11,8422}, {12,177}, {164,1698}, {167,7989}, {1210,5571}, {7670,7679}, {9780,9807}, {11681,11691}
X(12622) = midpoint of X(4) and X(12518)
X(12622) = orthologic center of these triangles: 4th Euler to 2nd midarc
X(12622) = reflection of X(12614) in X(5)
X(12622) = X(1)-of-4th-Euler-triangle
X(12622) = {X(8087), X(8088)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(21).
X(12623) lies on these lines: {2,12524}, {4,12519}, {5,12615}, {10,12267}, {11,21}, {442,1749}, {4197,12540}, {5046,12342}, {5499,12619}, {6599,7161}, {8582,12451}, {8728,12444}, {9780,12543}, {10887,12557}, {11681,12535}
X(12623) = midpoint of X(4) and X(12519)
X(12623) = reflection of X(12615) in X(5)
X(12623) = complement of X(12524)
The reciprocal orthologic center of these triangles is X(12508).
X(12624) lies on the nine-points circle and the line {2,12507}
X(12624) = complement of X(12507)
Orthologic centers: X(12625)-X(12808)
Centers X(12625)-X(12808) were contributed by César Eliud Lozada, March, 26, 2017.
The reciprocal orthologic center of these triangles is X(1).
X(12625) lies on these lines: {1,442}, {2,12437}, {4,519}, {8,9}, {10,3158}, {20,3928}, {57,4190}, {72,3586}, {78,4193}, {145,226}, {149,11682}, {200,1837}, {329,3621}, {355,6765}, {377,6173}, {388,3243}, {405,3679}, {497,6737}, {515,6762}, {517,5924}, {518,5691}, {527,3146}, {528,7991}, {674,12435}, {936,5722}, {938,5437}, {952,1490}, {1006,8715}, {1210,5438}, {1266,11851}, {1449,5716}, {1482,5715}, {1699,12635}, {1750,11519}, {1864,3893}, {2475,4654}, {2550,6738}, {2551,6743}, {2646,5231}, {2654,3190}, {2802,12691}, {2893,3875}, {3244,3487}, {3340,3434}, {3486,4847}, {3555,9613}, {3576,10916}, {3601,6734}, {3633,9612}, {3651,8666}, {3811,5587}, {3868,9579}, {3869,9580}, {3870,5086}, {3929,6872}, {3951,11114}, {3984,5046}, {4199,12642}, {4313,5745}, {4333,4880}, {4421,9588}, {4652,11015}, {4677,11113}, {4853,4863}, {5141,5219}, {5325,11106}, {5728,5836}, {5730,9614}, {5768,9841}, {5777,12645}, {5812,5844}, {5839,8804}, {5854,9897}, {5855,11531}, {5882,6908}, {5927,12448}, {5934,12633}, {5935,12634}, {6284,12526}, {6735,10395}, {6829,9624}, {6987,11362}, {7580,12513}, {8226,12607}, {8232,12630}, {8233,12638}, {8668,11517}, {10888,12546}, {11235,11522}
X(12625) = midpoint of X(3621) and X(12541)
X(12625) = reflection of X(i) in X(j) for these (i,j): (2136,8), (2900,3419), (3189,10), (3243,6601), (3633,10912), (6765,355), (11523,4), (12536,12437), (12632,12640)
X(12625) = anticomplement of X(12437)
X(12625) = complement of X(12536)
X(12625) = X(64)-of-2nd-extouch-triangle
X(12625) = X(6293)-of-excentral-triangle
X(12625) = excentral-to-2nd-extouch similarity image of X(2136)
X(12625) = 2nd-Conway-to-excentral similarity image of X(12536)
X(12625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,12536,12437), (8,390,5837), (8,950,9), (8,12632,12640), (10,3189,3158), (10,3488,5436), (145,5175,226), (377,11518,6173), (2321,5802,9), (2475,11520,4654), (3586,3632,72), (3870,5086,9578), (4863,10950,4853), (12632,12640,2136)
The reciprocal orthologic center of these triangles is X(10).
X(12626) lies on these lines: {1,1650}, {8,402}, {10,11831}, {30,944}, {145,4240}, {355,11897}, {515,12668}, {517,12113}, {519,1651}, {952,11251}, {2098,11906}, {2099,11905}, {2802,12729}, {3632,11852}, {3913,11848}, {5846,12583}, {10573,11913}, {10912,11903}, {10950,11909}, {11832,12135}, {11839,12195}, {11845,12245}, {11853,12410}, {11863,12454}, {11864,12455}, {11885,12495}, {11901,12627}, {11902,12628}, {11904,12635}, {11907,12636}, {11908,12637}, {11911,12645}, {11912,12647}, {11914,12648}, {11915,12649}
X(12626) = midpoint of X(145) and X(4240)
X(12626) = reflection of X(i) in X(j) for these (i,j): (8,402), (1650,1)
X(12626) = X(8)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12627) lies on these lines: {1,5591}, {6,8}, {10,11370}, {145,1271}, {355,6202}, {515,6258}, {517,5871}, {519,3641}, {944,11824}, {952,1161}, {1482,6215}, {2098,10925}, {2099,10923}, {2802,6263}, {3632,5589}, {3913,11497}, {5595,12410}, {5603,10514}, {5604,10513}, {5844,5875}, {7967,10517}, {8198,12454}, {8205,12455}, {8216,12636}, {8217,12637}, {9994,12495}, {10040,12647}, {10048,10573}, {10783,12245}, {10792,12195}, {10912,10919}, {10921,12635}, {10927,10950}, {10929,12648}, {10931,12649}, {11388,12135}, {11901,12626}, {11916,12645}
X(12627) = reflection of X(12628) in X(8)
X(12627) = X(8)-of-inner-Grebe-triangle
X(12627) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5689,5591), (145,1271,5605)
The reciprocal orthologic center of these triangles is X(10).
X(12628) lies on these lines: {1,5590}, {6,8}, {10,11371}, {145,1270}, {355,6201}, {515,6257}, {517,5870}, {519,3640}, {944,11825}, {952,1160}, {1482,6214}, {2098,10926}, {2099,10924}, {2802,6262}, {3632,5588}, {3913,11498}, {5594,12410}, {5603,10515}, {5605,10513}, {5844,5874}, {7967,10518}, {8199,12454}, {8206,12455}, {8218,12636}, {8219,12637}, {9995,12495}, {10041,12647}, {10049,10573}, {10784,12245}, {10793,12195}, {10912,10920}, {10922,12635}, {10928,10950}, {10930,12648}, {10932,12649}, {11389,12135}, {11902,12626}, {11917,12645}
X(12628) = reflection of X(12627) in X(8)
X(12628) = X(8)-of-outer-Grebe-triangle
X(12628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5688,5590), (145,1270,5604)
The reciprocal orthologic center of these triangles is X(1).
X(12629) lies on these lines: {1,2}, {3,2136}, {9,9957}, {20,12541}, {40,3880}, {56,3893}, {57,10914}, {63,3885}, {72,7962}, {84,517}, {165,8666}, {355,7956}, {518,5693}, {726,12652}, {937,1222}, {944,5732}, {952,1490}, {956,1697}, {999,1706}, {1000,5837}, {1058,5795}, {1320,11682}, {1385,3158}, {1388,3689}, {1420,5687}, {1449,5782}, {1476,3361}, {1482,5777}, {1768,2802}, {2077,8668}, {2324,5839}, {2975,3895}, {3189,5882}, {3243,5784}, {3333,5836}, {3340,3555}, {3421,12053}, {3434,9613}, {3436,9614}, {3576,3913}, {3646,10179}, {3754,10980}, {3813,5587}, {3878,5223}, {3928,12702}, {3984,5330}, {4298,9874}, {4512,5258}, {4863,10944}, {4866,10176}, {5082,10106}, {5119,5288}, {5436,6767}, {5437,7373}, {5657,12640}, {5697,10050}, {5720,12645}, {5731,12632}, {5780,10247}, {5854,6264}, {6282,12245}, {7675,12630}, {7967,8726}, {7987,8715}, {7997,11224}, {8111,12633}, {8112,12634}, {8227,12607}, {8234,12638}, {8235,12642}, {8951,10700}, {9785,12572}, {9819,12514}, {9845,9943}, {10864,12448}, {10884,12536}, {11526,12559}
X(12629) = midpoint of X(i) and X(j) for these {i,j}: {1,11519}, {20,12541}, {145,6764}, {3680,6762}
X(12629) = reflection of X(i) in X(j) for these (i,j): (40,12513), (2136,3), (3189,5882), (3913,11260), (6264,11256), (6765,1), (7982,10912), (11523,1482)
X(12629) = X(64)-of-hexyl-triangle
X(12629) = excentral-to-hexyl similarity image of X(2136)
X(12629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,8,936), (1,3632,200), (1,3679,8583), (1,4853,9623), (1,4882,997), (1,4915,10), (1,12127,3244), (997,3625,4882), (3333,11525,5836), (3870,4861,1), (3913,11260,3576)
The reciprocal orthologic center of these triangles is X(1).
X(12630) lies on these lines: {7,145}, {8,344}, {9,3621}, {100,1617}, {142,3623}, {390,519}, {516,3633}, {517,12669}, {518,3644}, {956,4313}, {1445,2136}, {2550,3241}, {2802,12755}, {3189,4308}, {3244,11038}, {3632,5686}, {3813,7679}, {3870,5226}, {3880,7672}, {3893,5572}, {3913,7677}, {3935,5328}, {4321,12127}, {4326,11519}, {4344,4649}, {4413,10580}, {4678,6666}, {4779,4899}, {4863,10578}, {5759,5844}, {5817,12645}, {5836,11025}, {5854,12730}, {6049,8732}, {6737,7320}, {7675,12629}, {7676,12513}, {7678,12607}, {8232,12625}, {8237,12638}, {8238,12642}, {8385,12633}, {8386,12634}, {8389,12646}, {10865,12448}, {10889,12546}
X(12630) = reflection of X(i) in X(j) for these (i,j): (7,145), (3621,9), (3893,5572)
X(12630) = X(64)-of-Honsberger-triangle
X(12630) = excentral-to-Honsberger similarity image of X(2136)
X(12630) = {X(3189), X(9797)}-harmonic conjugate of X(4308)
The reciprocal orthologic center of these triangles is X(12632).
X(12631) lies on these lines: {3,12333}, {9,3295}, {10,6767}, {55,9898}, {100,5558}, {119,3851}, {142,3913}, {214,7373}, {442,5082}, {938,1145}, {999,8000}, {3303,3983}, {3870,5920}, {5687,9874}, {6184,9605}, {6244,12120}, {6260,12699}, {6744,12640}, {8001,8273}, {10679,12684}, {11530,12654}
X(12631) = midpoint of X(7160) and X(12658)
X(12631) = reflection of X(3) in X(12333)
The reciprocal orthologic center of these triangles is X(12631).
X(12632) lies on these lines: {1,11024}, {2,3303}, {8,9}, {20,519}, {40,6764}, {57,9797}, {65,145}, {100,5265}, {144,12125}, {200,9785}, {442,5082}, {497,8165}, {518,9961}, {528,3146}, {529,5059}, {952,12684}, {962,1750}, {1706,10580}, {2551,8168}, {2899,6552}, {3158,3616}, {3174,11038}, {3241,3680}, {3244,11034}, {3434,5261}, {3486,3893}, {3522,12513}, {3523,8715}, {3621,11684}, {3623,10912}, {3632,4294}, {3633,4293}, {3832,12607}, {3871,5281}, {4193,5274}, {4297,11519}, {4309,4677}, {4313,4853}, {4314,4915}, {4315,12127}, {4452,7195}, {4673,7172}, {4882,12575}, {5068,11235}, {5141,10528}, {5177,11239}, {5731,12629}, {5815,10624}, {5919,12448}, {6743,9819}, {6762,9778}, {8666,10304}, {10385,11106}, {10465,12546}
X(12632) = reflection of X(i) in X(j) for these (i,j): (8,2136), (145,3189), (390,7674), (962,6765), (3680,12437), (6764,40), (11519,4297), (12541,1), (12625,12640)
X(12632) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8,5250,5686), (2136,12625,12640), (3680,12437,3241), (12625,12640,8)
The reciprocal orthologic center of these triangles is X(1).
X(12633) lies on these lines: {8,8390}, {145,8113}, {363,2136}, {519,9836}, {2802,12759}, {3244,11039}, {3621,11685}, {3680,11527}, {3813,8380}, {3913,8109}, {5836,11026}, {5854,12733}, {5934,12625}, {8107,12513}, {8111,12629}, {8140,11519}, {8377,12607}, {8385,12630}, {8391,12642}, {9783,12541}, {11854,12437}, {11856,12448}, {11886,12536}, {11892,12546}, {11922,12638}
X(12633) = reflection of X(12634) in X(11519)
X(12633) = X(64)-of-inner-Hutson-triangle
X(12633) = excentral-to-inner-Hutson similarity image of X(2136)
The reciprocal orthologic center of these triangles is X(1).
X(12634) lies on these lines: {145,8114}, {519,9837}, {2802,12760}, {3244,11040}, {3621,11686}, {3813,8381}, {3913,8110}, {5836,11027}, {5854,12734}, {5935,12625}, {8108,12513}, {8112,12629}, {8140,11519}, {8378,12607}, {8386,12630}, {11855,12437}, {11857,12448}, {11887,12536}, {11893,12546}, {11925,12638}, {11926,12642}
X(12634) = reflection of X(12633) in X(11519)
X(12634) = X(64)-of-outer-Hutson-triangle
X(12634) = excentral-to-outer-Hutson similarity image of X(2136)
The reciprocal orthologic center of these triangles is X(10).
X(12635) lies on these lines: {1,6}, {2,11281}, {3,758}, {8,12}, {10,3940}, {11,12649}, {36,3901}, {40,4421}, {46,4018}, {55,3869}, {56,1259}, {63,2646}, {65,78}, {142,12447}, {145,497}, {200,3340}, {210,3984}, {226,5794}, {320,7185}, {329,3486}, {354,11520}, {355,381}, {377,3649}, {404,5221}, {474,5902}, {480,7672}, {515,5812}, {516,12437}, {517,3811}, {527,4297}, {528,962}, {529,944}, {908,1837}, {912,12114}, {936,3812}, {938,3816}, {940,2650}, {942,997}, {952,10526}, {959,1257}, {965,2294}, {976,5710}, {986,4255}, {993,3927}, {999,3874}, {1012,5693}, {1042,1818}, {1043,5327}, {1046,4252}, {1125,5791}, {1155,4855}, {1159,3754}, {1215,5793}, {1265,3932}, {1320,7319}, {1385,11194}, {1389,10599}, {1698,5425}, {1699,12625}, {1706,10107}, {1788,3035}, {1848,5130}, {2136,11531}, {2171,3713}, {2271,3735}, {2800,10306}, {2802,8148}, {2932,11571}, {3057,3870}, {3149,6326}, {3158,7991}, {3190,10571}, {3207,3509}, {3218,5204}, {3241,5330}, {3295,3878}, {3303,3877}, {3304,3873}, {3339,5438}, {3419,12047}, {3452,6738}, {3496,4258}, {3560,5694}, {3601,4640}, {3612,3916}, {3617,3711}, {3632,10827}, {3633,9614}, {3671,5880}, {3678,9708}, {3680,11224}, {3715,5260}, {3742,8583}, {3746,3899}, {3813,5603}, {3880,6765}, {3881,7373}, {3884,6767}, {3890,3957}, {3894,5563}, {3924,4383}, {3928,7987}, {3930,4513}, {4101,10371}, {4189,11684}, {4190,11246}, {4299,10609}, {4301,5853}, {4313,5698}, {4345,9797}, {4428,5250}, {4662,9623}, {4848,6745}, {4860,5253}, {4880,7280}, {5086,10895}, {5087,9581}, {5703,6690}, {5704,6667}, {5719,10198}, {5720,7686}, {5731,5852}, {5734,6764}, {5761,7680}, {5780,10175}, {5844,10942}, {5846,12587}, {5851,12246}, {5854,10698}, {5886,10916}, {5887,11496}, {5905,7354}, {6049,6068}, {6265,10680}, {6282,9943}, {6284,11415}, {6734,11375}, {6769,7971}, {6872,10543}, {6943,9803}, {7080,8256}, {8168,10914}, {8666,10246}, {8715,12702}, {8834,10699}, {9669,11813}, {9812,12536}, {10176,11108}, {10474,11679}, {10522,10944}, {10523,10573}, {10786,12245}, {10795,12195}, {10830,12410}, {10872,12495}, {10921,12627}, {10922,12628}, {10951,12636}, {10952,12637}, {10954,12647}, {10955,12648}, {11391,12135}, {11495,12520}, {11868,12455}, {11904,12626}
X(12635) = midpoint of X(i) and X(j) for these {i,j}: {1,11523}, {962,3189}, {2136,11531}, {6765,7982}, {6769,7971}
X(12635) = reflection of X(i) in X(j) for these (i,j): (8,12607), (3913,3811), (6762,11260), (10912,1482), (12513,1), (12702,8715)
X(12635) = X(8)-of-outer-Johnson-triangle
X(12635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,72,958), (1,960,1001), (1,4867,5730), (1,5692,405), (1,5730,5289), (1,5904,956), (1,6762,11260), (8,3485,2886), (65,78,1376), (72,958,5220), (145,3436,10950), (200,3340,5836), (226,6737,5794), (936,11529,3812), (2646,3962,63), (3868,4511,56), (4018,5440,46), (6762,11260,12513), (11929,12645,355), (12447,12563,142)
The reciprocal orthologic center of these triangles is X(10).
X(12636) lies on these lines: {1,8214}, {8,493}, {10,11377}, {145,6462}, {355,8212}, {517,9838}, {519,12152}, {944,11828}, {952,10669}, {1482,8220}, {2098,11932}, {2099,11930}, {2802,12741}, {3632,8188}, {3913,11503}, {5846,12590}, {6339,8211}, {6461,12637}, {8194,12410}, {8201,12454}, {8208,12455}, {8216,12627}, {8218,12628}, {10573,11953}, {10875,12495}, {10912,10945}, {10950,11947}, {10951,12635}, {11394,12135}, {11840,12195}, {11846,12245}, {11907,12626}, {11949,12645}, {11951,12647}, {11955,12648}, {11957,12649}
X(12636) = X(8)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(10).
X(12637) lies on these lines: {1,8215}, {8,494}, {10,11378}, {145,6463}, {355,8213}, {517,9839}, {519,12153}, {944,11829}, {952,10673}, {1482,8221}, {2098,11933}, {2099,11931}, {2802,12742}, {3632,8189}, {3913,11504}, {5846,12591}, {6339,8210}, {6461,12636}, {8195,12410}, {8202,12454}, {8209,12455}, {8217,12627}, {8219,12628}, {10573,11954}, {10876,12495}, {10912,10946}, {10950,11948}, {10952,12635}, {11395,12135}, {11841,12195}, {11847,12245}, {11908,12626}, {11950,12645}, {11952,12647}, {11956,12648}, {11958,12649}
X(12637) = X(8)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(1).
X(12638) lies on these lines: {8,7090}, {145,8243}, {517,12681}, {519,7596}, {2136,8231}, {2802,12768}, {3244,11042}, {3621,11687}, {3680,7595}, {3813,8230}, {3880,9808}, {3913,8225}, {5836,11030}, {5854,12744}, {8224,12513}, {8228,12607}, {8233,12625}, {8234,12629}, {8237,12630}, {8244,11519}, {8246,12642}, {9789,12541}, {10858,12437}, {10867,12448}, {10885,12536}, {10891,12546}, {11922,12633}, {11925,12634}, {11996,12646}
X(12638) = X(64)-of-2nd-Pamfilos-Zhou-triangle
X(12638) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(2136)
The reciprocal orthologic center of these triangles is X(6598).
X(12639) lies on these lines: {2,6597}, {3,12342}, {9,10266}, {10,12267}, {100,6599}, {214,11263}, {11530,12657}
X(12639) = midpoint of X(i) and X(j) for these {i,j}: {100,6599}, {10266,12660}
X(12639) = complement of X(6597)
The reciprocal orthologic center of these triangles is X(12641).
X(12640) lies on these lines: {1,6692}, {2,3680}, {3,519}, {8,9}, {10,496}, {65,10427}, {100,1476}, {119,946}, {142,5836}, {145,1420}, {214,3244}, {442,10914}, {517,6260}, {527,7991}, {529,5493}, {936,1000}, {993,8668}, {1125,10912}, {1145,1210}, {1329,4342}, {2098,6745}, {2551,9819}, {3057,3452}, {3189,3632}, {3617,12541}, {3625,3647}, {3679,5084}, {3740,12448}, {3885,4193}, {3890,5316}, {3893,4847}, {4190,10106}, {4301,12607}, {4677,11111}, {4853,5745}, {5542,10107}, {5657,12629}, {5919,8582}, {6556,8055}, {6600,6738}, {6743,8168}, {6744,12631}, {6765,12245}, {6848,7982}, {7080,7962}, {8256,11019}, {10164,11260}
X(12640) = midpoint of X(i) and X(j) for these {i,j}: {8,2136}, {100,12641}, {3189,3632}, {6765,12245}, {12625,12632}
X(12640) = reflection of X(i) in X(j) for these (i,j): (946,10915), (4301,12607), (5882,8715), (10912,1125), (12437,3913)
X(12640) = complement of X(3680)
X(12640) = X(4)-of-excenters-midpoints-triangle
X(12640) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8,1697,5795), (8,3895,950), (8,12632,12625), (2136,12625,12632), (3057,6736,3452), (3885,6735,12053)
The reciprocal orthologic center of these triangles is X(12640).
X(12641) lies on the Feuerbach hyperbola and these lines: {1,1145}, {4,2802}, {7,12648}, {8,4939}, {9,4534}, {11,3680}, {79,12749}, {80,3880}, {84,952}, {90,3632}, {100,1476}, {104,519}, {119,3577}, {149,7319}, {392,5559}, {528,3062}, {1000,3898}, {1156,5853}, {1317,3158}, {1320,6735}, {1389,10915}, {1392,5552}, {2320,5281}, {2800,10309}, {2801,10307}, {2932,3913}, {3036,4900}, {3893,6598}, {5541,7284}, {5554,7320}, {5665,10956}, {10305,12245}, {11219,11256}
X(12641) = reflection of X(i) in X(j) for these (i,j): (100,12640), (3680,11), (7972,3913)
X(12641) = isogonal conjugate of X(5193)
X(12641) = antigonal conjugate of X(3680)
X(12641) = X(4)-of-2nd-Schiffler-triangle
X(12641) = antipode of X(3680) in Feuerbach hyperbola
The reciprocal orthologic center of these triangles is X(1).
X(12642) lies on these lines: {8,21}, {145,1284}, {256,3680}, {517,12683}, {519,9840}, {846,2136}, {1469,11520}, {2292,3880}, {2802,12770}, {3244,11043}, {3621,11688}, {3813,5051}, {4199,12625}, {4220,12513}, {4685,8731}, {5836,11031}, {5854,12746}, {8229,12607}, {8235,12629}, {8238,12630}, {8245,11519}, {8246,12638}, {8391,12633}, {8425,12646}, {9791,12541}, {10868,12448}, {10892,12546}, {11926,12634}
X(12642) = X(64)-of-1st-Sharygin-triangle
X(12642) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13252)
X(12642) = excentral-to-1st-Sharygin similarity image of X(2136)
The reciprocal orthologic center of these triangles is X(1).
X(12643) lies on the cubic K201 and these lines: {1,236}, {8,188}, {145,2089}, {177,3680}, {517,8095}, {519,8091}, {2136,8078}, {3244,11044}, {3621,11690}, {3813,8087}, {3880,8093}, {3893,10503}, {3913,8077}, {5836,11032}, {5854,8097}, {5881,9836}, {6553,10490}, {7028,8422}, {8075,12513}, {8085,12607}, {8089,11519}, {8733,12437}, {9793,12541}, {11858,12448}, {11888,12536}, {11894,12546}
X(12643) = reflection of X(12644) in X(1)
X(12643) = X(64)-of-tangential-midarc-triangle
X(12643) = excentral-to-tangential-midarc similarity image of X(2136)
X(12643) = {X(8), X(8241)}-harmonic conjugate of X(188)
The reciprocal orthologic center of these triangles is X(1).
X(12644) lies on the cubic K201 and these lines: {1,236}, {145,174}, {1483,8130}, {2802,12772}, {3241,11924}, {3243,11535}, {3244,8351}, {3621,8125}, {3623,8126}, {3680,11899}, {3913,7588}, {5836,11033}, {5844,8129}, {8734,12437}, {11859,12448}, {11895,12546}
X(12644) = reflection of X(12643) in X(1)
X(12644) = X(64)-of-2nd-tangential-midarc-triangle
X(12644) = excentral-to-2nd-tangential-midarc similarity image of X(2136)
X(12644) = {X(145), X(174)}-harmonic conjugate of X(12646)
The reciprocal orthologic center of these triangles is X(10).
X(12645) lies on the cubic K201 and these lines: {1,1656}, {2,1483}, {3,8}, {4,3621}, {5,145}, {10,3526}, {30,12245}, {40,3534}, {80,2098}, {119,3813}, {140,3617}, {355,381}, {382,517}, {388,1159}, {499,1317}, {515,1657}, {518,11898}, {631,4678}, {912,10914}, {962,3830}, {999,10573}, {1351,5846}, {1352,9053}, {1385,3679}, {1388,7972}, {1484,4193}, {1598,12135}, {1699,11278}, {2099,9654}, {2136,7330}, {2802,12747}, {2937,9798}, {3086,11545}, {3090,3623}, {3167,9933}, {3241,5055}, {3244,5079}, {3295,7489}, {3421,6928}, {3445,6788}, {3576,4668}, {3579,4816}, {3616,5070}, {3622,3628}, {3626,5882}, {3633,5072}, {3635,10175}, {3653,4745}, {3654,4297}, {3655,4669}, {3851,5603}, {3871,6914}, {3880,5887}, {3913,11849}, {4691,10165}, {4701,11362}, {4853,5534}, {5048,10826}, {5076,12699}, {5082,6923}, {5176,5730}, {5531,11014}, {5694,5697}, {5708,10106}, {5720,12629}, {5722,5780}, {5727,9957}, {5777,12625}, {5779,5853}, {5811,12541}, {5817,12630}, {5854,10738}, {6147,11041}, {6265,11256}, {6862,10528}, {6913,12000}, {6918,12001}, {6941,11698}, {6958,7080}, {6959,10529}, {6971,10943}, {6980,10942}, {7517,12410}, {8168,12114}, {8200,11876}, {8207,11875}, {9301,12495}, {9858,10202}, {10525,10742}, {10827,11011}, {10895,11009}, {11499,12513}, {11842,12195}, {11911,12626}, {11916,12627}, {11917,12628}, {11949,12636}, {11950,12637}
X(12645) = midpoint of X(i) and X(j) for these {i,j}: {4,3621}, {3632,5881}
X(12645) = reflection of X(i) in X(j) for these (i,j): (3,8), (145,5), (944,5690), (1482,355), (1657,12702), (3655,4669), (5697,5694), (5882,3626), (8148,4), (11362,4701)
X(12645) = anticomplement of X(1483)
X(12645) = X(8)-of-X3-ABC-reflections-triangle
X(12645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5790,1656), (5,145,10247), (8,944,5690), (10,10246,3526), (80,2098,9669), (355,1482,381), (355,10912,11928), (355,12635,11929), (944,5690,3), (3090,3623,10283), (3241,5818,5901), (3617,7967,140), (5818,5901,5055), (10573,10944,999), (10950,12647,3295)
The reciprocal orthologic center of these triangles is X(1).
X(12646) lies on the cubic K201 and these lines: {1,188}, {8,178}, {145,174}, {173,2136}, {177,3680}, {517,12685}, {519,8351}, {1483,8129}, {2802,12774}, {3621,8126}, {3623,8125}, {3813,8382}, {3880,12445}, {3893,10502}, {3913,7587}, {5836,8083}, {5844,8130}, {5854,12748}, {7593,12625}, {8389,12630}, {8423,11519}, {8425,12642}, {8729,12437}, {11860,12448}, {11890,12536}, {11891,12541}, {11896,12546}, {11996,12638}
X(12646) = X(64)-of-Yff-central-triangle
X(12646) = excentral-to-Yff-central similarity image of X(2136)
X(12646) = {X(483),X(3082)}-harmonic conjugate of X(236)
X(12646) = {X(145), X(174)}-harmonic conjugate of X(12644)
The reciprocal orthologic center of these triangles is X(10).
X(12647) lies on these lines: {1,2}, {3,10944}, {4,5559}, {5,2098}, {11,5790}, {12,1482}, {20,11010}, {35,944}, {36,3476}, {40,4299}, {46,4317}, {47,5255}, {55,952}, {56,5690}, {65,10044}, {79,7317}, {80,497}, {140,1388}, {329,3899}, {355,1479}, {390,9897}, {474,8256}, {484,4293}, {495,2099}, {515,1709}, {517,1478}, {611,5846}, {912,12430}, {942,11045}, {946,6968}, {950,6976}, {956,8069}, {958,11508}, {962,3585}, {982,1772}, {1056,5902}, {1145,1376}, {1155,3654}, {1317,5432}, {1320,11680}, {1621,12531}, {1697,4309}, {1699,8275}, {1734,2401}, {1770,7991}, {1788,5563}, {1837,9957}, {2478,3884}, {2800,12115}, {2802,3434}, {2886,5854}, {3036,3816}, {3245,3474}, {3295,7489}, {3336,3600}, {3338,4848}, {3419,3880}, {3421,5692}, {3436,3878}, {3475,5425}, {3485,11009}, {3486,3746}, {3586,9819}, {3612,5882}, {3753,5570}, {3877,5176}, {3885,5086}, {3898,10073}, {4295,5270}, {4316,9778}, {4333,5493}, {4351,8270}, {4421,10609}, {4857,9785}, {5010,5731}, {5048,5886}, {5082,10629}, {5218,7967}, {5261,11280}, {5281,9803}, {5330,8070}, {5443,10588}, {5445,7288}, {5587,6973}, {5599,11880}, {5600,11879}, {5603,7951}, {5687,8071}, {5691,9898}, {5722,5919}, {5726,11224}, {5730,12607}, {5794,10914}, {5818,7741}, {5884,10805}, {6361,10483}, {6702,10584}, {6825,11014}, {6982,7982}, {7354,12702}, {8148,9654}, {8200,11874}, {8207,11873}, {9612,11531}, {9956,11376}, {10037,12410}, {10038,12495}, {10040,12627}, {10041,12628}, {10074,10269}, {10801,12195}, {10826,12053}, {10954,12635}, {10966,11499}, {11011,11374}, {11238,12019}, {11249,11501}, {11252,11870}, {11253,11869}, {11398,12135}, {11877,12454}, {11878,12455}, {11912,12626}, {11951,12636}, {11952,12637}, {12751,12758}
X(12647) = midpoint of X(8) and X(12648)
X(12647) = reflection of X(i) in X(j) for these (i,j): (1478,5252), (2099,495), (4302,5119)
X(12647) = X(8)-of-inner-Yff-triangle
X(12647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,8,10573), (1,10,499), (1,1737,10072), (1,3679,1737), (1,10039,498), (46,10106,4317), (145,3085,1), (355,3057,1479), (1317,5432,10246), (1697,5881,10572), (1697,10572,4309), (3085,10527,10320), (3295,12645,10950), (3475,11041,5425), (3476,5657,36), (3632,3679,4915), (6929,10947,1479), (7991,9613,1770), (10106,11362,46), (10320,10527,499)
The reciprocal orthologic center of these triangles is X(10).
X(12648) lies on these lines: {1,2}, {4,3885}, {7,12641}, {12,10912}, {40,11919}, {65,10940}, {100,1470}, {119,1320}, {355,6957}, {377,10914}, {388,7702}, {497,5176}, {515,3895}, {517,5905}, {908,7962}, {942,11047}, {944,3871}, {952,1012}, {962,6256}, {999,1145}, {1000,3421}, {1478,2802}, {1482,1532}, {1697,6872}, {2077,5731}, {2098,10958}, {2099,5854}, {2478,9957}, {2551,3890}, {3057,3436}, {3218,3359}, {3304,8256}, {3434,3880}, {3680,6871}, {3868,6916}, {3893,5794}, {3913,10944}, {4188,4308}, {4190,10106}, {4345,5748}, {4917,12437}, {5046,9785}, {5123,10584}, {5175,12541}, {5187,12053}, {5193,5435}, {5559,5904}, {5657,10269}, {5697,11415}, {5844,6907}, {5846,12594}, {5853,8545}, {5902,11046}, {6913,12000}, {6931,11373}, {6939,10596}, {7982,12608}, {7991,10970}, {10247,11729}, {10524,10827}, {10803,12195}, {10834,12410}, {10878,12495}, {10929,12627}, {10930,12628}, {10950,10965}, {10955,12635}, {11400,12135}, {11881,12454}, {11882,12455}, {11914,12626}, {11955,12636}, {11956,12637}
X(12648) = reflection of X(i) in X(j) for these (i,j): (8,12647), (145,3870), (3434,5252)
X(12648) = X(8)-of-inner-Yff-tangents-triangle
X(12648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,8,5554), (1,6735,2), (1,10915,5552), (8,145,12649), (145,10528,1), (1000,3421,3877), (10528,10530,5552)
The reciprocal orthologic center of these triangles is X(10).
X(12649) lies on these lines: {1,2}, {4,912}, {7,2475}, {11,12635}, {20,3218}, {21,3488}, {29,1069}, {40,11920}, {57,4190}, {63,950}, {65,3434}, {69,5016}, {72,2478}, {75,5738}, {81,5716}, {100,1788}, {144,5809}, {149,151}, {224,2900}, {225,11851}, {226,6871}, {273,5174}, {307,3875}, {329,5046}, {346,8557}, {354,5794}, {355,3555}, {376,11015}, {377,942}, {382,12690}, {388,3873}, {405,12433}, {411,944}, {452,3219}, {496,5730}, {497,3869}, {515,12687}, {517,6836}, {518,1837}, {758,1479}, {894,5807}, {908,5187}, {946,6870}, {952,3149}, {956,11344}, {1056,3889}, {1058,3877}, {1068,1897}, {1229,4696}, {1265,4358}, {1320,6943}, {1331,1724}, {1445,4848}, {1446,6604}, {1478,3874}, {1482,6831}, {1512,5534}, {1895,5081}, {1936,7538}, {1993,3562}, {2098,5855}, {2099,3813}, {2287,5839}, {2476,3487}, {2550,5178}, {2551,3681}, {2802,12750}, {2899,3952}, {2975,3486}, {3057,10936}, {3091,5804}, {3146,9799}, {3152,3210}, {3243,9578}, {3254,7319}, {3452,3984}, {3485,11680}, {3583,3901}, {3585,3894}, {3711,9711}, {3832,5715}, {3871,5657}, {3876,5084}, {3885,6865}, {3895,11362}, {3911,4855}, {3913,11510}, {3927,11113}, {3940,4187}, {3951,12572}, {4018,12699}, {4188,5435}, {4189,4313}, {4304,4652}, {4430,6894}, {4452,5932}, {4661,5815}, {4863,5836}, {4881,5265}, {5057,5225}, {5059,10430}, {5141,5226}, {5154,5748}, {5177,11036}, {5249,11518}, {5279,5802}, {5440,6921}, {5603,6828}, {5698,11684}, {5708,11112}, {5720,6953}, {5727,6762}, {5731,11012}, {5758,6840}, {5761,6830}, {5770,6906}, {5777,6957}, {5787,10431}, {5818,6991}, {5844,6922}, {5846,12595}, {5887,10531}, {6224,10074}, {6585,11491}, {6601,7672}, {6855,10595}, {6864,10597}, {6897,10202}, {6918,12001}, {6933,11374}, {6988,7967}, {7466,7718}, {7991,10971}, {10524,10826}, {10804,12195}, {10835,12410}, {10879,12495}, {10912,10949}, {10931,12627}, {10932,12628}, {10950,10966}, {11401,12135}, {11682,12053}, {11883,12454}, {11884,12455}, {11915,12626}, {11957,12636}, {11958,12637}, {12047,12559}
X(12649) = reflection of X(i) in X(j) for these (i,j): (8,10573), (78,1210), (3436,1837), (5730,496), (6224,10074), (11415,1479), (11682,12053)
X(12649) = isogonal conjugate of X(34430)
X(12649) = complement of X(20013)
X(12649) = anticomplement of X(78)
X(12649) = X(8)-of-outer-Yff-tangents-triangle
X(12649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,6734,2), (1,10916,10527), (4,3868,5905), (7,5175,2475), (8,145,12648), (8,938,2), (8,6764,3621), (10,3870,10528), (63,950,6872), (72,5722,2478), (78,1210,2), (145,10528,3870), (145,10529,1), (908,9581,5187), (942,3419,377), (1737,3811,5552), (1788,3189,100), (3873,5086,388), (9581,11523,908), (10529,10530,10527)
The reciprocal orthologic center of these triangles is X(72).
X(12650) lies on these lines: {1,4}, {3,1706}, {8,6245}, {10,6926}, {30,12700}, {40,956}, {84,517}, {145,9799}, {165,5450}, {200,5881}, {355,936}, {474,3576}, {519,6769}, {942,3577}, {952,5787}, {971,1482}, {993,10268}, {1012,1697}, {1125,6964}, {1158,6763}, {1385,6918}, {1420,3149}, {1467,4311}, {1512,10785}, {1698,6967}, {1709,5697}, {2057,5176}, {2098,12688}, {2099,12680}, {2136,10306}, {2800,3901}, {2802,2950}, {2829,6264}, {3057,12705}, {3062,12666}, {3295,7966}, {3333,7686}, {3427,6737}, {3555,6001}, {3624,6983}, {3679,12616}, {4187,5587}, {4915,11362}, {5657,6705}, {5731,6904}, {5732,5832}, {5758,5924}, {5795,6865}, {5806,7373}, {5842,12565}, {6735,6890}, {6796,6940}, {6831,9578}, {6975,7989}, {7962,12672}, {7994,12245}, {8148,12684}, {9845,11529}, {9942,11518}, {9948,11519}, {9960,11520}, {11521,12547}, {11523,12664}, {11526,12669}, {11532,12681}, {11533,12683}, {11535,12685}, {11682,12528}
X(12650) = midpoint of X(i) and X(j) for these {i,j}: {145,9799}, {7982,10864}, {7992,11531}, {8148,12684}
X(12650) = reflection of X(i) in X(j) for these (i,j): (8,6245), (40,12114), (1490,1), (2136,10306), (7971,1482), (7991,1158), (12667,946)
X(12650) = X(68)-of-excenters-reflections-triangle
X(12650) = excentral-to-excenters-reflections similarity image of X(1490)
X(12650) = excenters-reflections-isotomic conjugate of X(12652)
X(12650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,944,10106), (5691,9614,4), (9845,11529,12675)
The reciprocal orthologic center of these triangles is X(65).
X(12651) lies on these lines: {1,7}, {3,10582}, {4,200}, {9,7957}, {10,7994}, {40,405}, {72,11372}, {78,9812}, {145,9800}, {165,3833}, {354,9841}, {382,5534}, {388,10388}, {443,946}, {517,3927}, {936,1699}, {942,10860}, {956,6766}, {1467,3474}, {1490,5842}, {1698,6886}, {1750,3811}, {1998,6895}, {2098,9850}, {2999,6996}, {3062,12528}, {3091,8580}, {3146,3870}, {3174,6253}, {3243,12680}, {3340,12711}, {3361,6909}, {3522,4666}, {3555,6001}, {3679,12617}, {3841,7988}, {3868,7992}, {3957,5059}, {4420,10248}, {5231,6847}, {5234,6912}, {5268,7385}, {5290,6925}, {5436,5584}, {5531,10724}, {5691,6765}, {5806,6244}, {7962,12709}, {7987,12511}, {7989,12558}, {9851,11224}, {9943,11518}, {9949,11519}, {9961,11520}, {10398,12432}, {10857,12512}, {11521,12548}, {11522,12609}, {11523,12688}, {11526,12706}, {11527,12707}, {11528,12708}, {11529,12710}, {11532,12712}, {11533,12713}, {11535,12716}, {11682,12529}, {11899,12715}
X(12651) = midpoint of X(145) and X(9800)
X(12651) = reflection of X(i) in X(j) for these (i,j): (20,4314), (40,11496), (4295,4301), (7991,12514), (12526,12705), (12565,1)
X(12651) = excentral-to-excenters-reflections similarity image of X(12565)
X(12651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,2951,10884), (1,4292,4321), (1,4294,4326), (4,6769,200), (40,11496,4512), (946,6282,8583), (4319,4332,1), (4336,4348,1), (7982,10864,3555)
The reciprocal orthologic center of these triangles is X(65).
X(12652) lies on these lines: {1,7}, {40,238}, {43,7994}, {105,165}, {145,9801}, {200,4388}, {517,1351}, {612,9812}, {614,9778}, {651,7673}, {726,12629}, {936,4660}, {982,10860}, {984,11372}, {1038,12701}, {1279,11495}, {1697,9440}, {1699,5268}, {1743,1766}, {1750,3961}, {3057,6180}, {3177,3729}, {3339,8915}, {3340,12723}, {3679,12618}, {3749,7580}, {3923,9623}, {3976,9841}, {5223,9355}, {7290,9441}, {7962,12721}, {7996,11531}, {8270,9580}, {9944,11518}, {9950,11519}, {9962,11520}, {11521,12549}, {11522,12610}, {11523,12689}, {11526,12718}, {11527,12719}, {11528,12720}, {11529,12722}, {11532,12724}, {11533,12725}, {11535,12728}, {11682,12530}, {11899,12727}
X(12652) = midpoint of X(i) and X(j) for these {i,j}: {145,9801}, {7996,11531}
X(12652) = reflection of X(i) in X(j) for these (i,j): (1721,1), (7991,1766)
X(12652) = X(317)-of-excenters-reflections-triangle
X(12652) = excentral-to-excenters-reflections similarity image of X(1721)
X(12652) = excenters-reflections-isotomic conjugate of X(12650)
X(12652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (390,2263,1), (1448,12575,1), (4318,4319,1), (4320,9785,1)
The reciprocal orthologic center of these triangles is X(8).
X(12653) lies on these lines: {1,88}, {8,11524}, {11,3679}, {40,12737}, {80,3632}, {104,7991}, {119,11522}, {145,9802}, {149,519}, {153,4301}, {165,11715}, {191,956}, {517,1768}, {528,3243}, {952,3627}, {1023,4919}, {1145,1698}, {1317,3340}, {1387,3624}, {1482,6326}, {1699,12751}, {2093,10074}, {2170,4752}, {2771,8148}, {2800,3901}, {2829,9589}, {2932,5563}, {3057,5251}, {3244,6224}, {3577,5660}, {3656,11698}, {3884,5506}, {3894,11571}, {3899,5223}, {4413,6797}, {4677,10707}, {4816,12019}, {5531,10698}, {5881,10738}, {6154,11034}, {6713,9588}, {6762,11256}, {9612,12749}, {9898,12654}, {9945,11518}, {9951,11519}, {9963,11520}, {10265,12245}, {10825,11521}, {11523,12690}, {11526,12730}, {11527,12733}, {11528,12734}, {11532,12744}, {11533,12746}, {11535,12748}, {11682,12531}, {12409,12657}
X(12653) = midpoint of X(i) and X(j) for these {i,j}: {145,9802}, {7993,11531}
X(12653) = reflection of X(i) in X(j) for these (i,j): (1,1320), (40,12737), (153,4301), (1768,6264), (3632,80), (4677,10707), (5531,10698), (5541,1), (5881,10738), (6154,12735), (6224,3244), (6326,1482), (6762,11256), (7991,104), (9897,149), (12245,10265)
X(12653) = X(74)-of-excenters-reflections-triangle
X(12653) = excentral-to-excenters-reflections similarity image of X(5541)
X(12653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (244,10700,1), (4792,10700,244), (5531,11224,10698)
The reciprocal orthologic center of these triangles is X(3555).
X(12654) lies on these lines: {1,12521}, {72,4853}, {145,9804}, {200,9624}, {936,1387}, {1482,12670}, {3090,4882}, {3243,5784}, {3679,12620}, {3680,7160}, {4002,10582}, {5920,7962}, {6264,10609}, {6765,11374}, {7991,12516}, {8001,11531}, {9898,12653}, {9953,11519}, {11224,12756}, {11518,12439}, {11520,12537}, {11521,12552}, {11522,12612}, {11523,12692}, {11525,12260}, {11530,12631}, {11682,12533}
X(12654) = midpoint of X(i) and X(j) for these {i,j}: {145,9804}, {8001,11531}
X(12654) = reflection of X(i) in X(j) for these (i,j): (7991,12516), (12658,1)
The reciprocal orthologic center of these triangles is X(3555).
X(12655) lies on these lines: {1,12522}, {145,12542}, {3679,12621}, {7991,12517}, {11518,12442}, {11519,12449}, {11520,12538}, {11521,12553}, {11522,12613}, {11523,12693}, {11682,12534}
X(12655) = midpoint of X(145) and X(12542)
X(12655) = reflection of X(i) in X(j) for these (i,j): (7991,12517), (12659,1)
The reciprocal orthologic center of these triangles is X(1).
X(12656) lies on these lines: {1,164}, {145,9807}, {167,11531}, {177,3340}, {3679,12622}, {7670,11526}, {7962,8422}, {7991,12518}, {11519,12450}, {11520,12539}, {11521,12554}, {11682,11691}
X(12656) = midpoint of X(i) and X(j) for these {i,j}: {145,9807}, {167,11531}
X(12656) = reflection of X(i) in X(j) for these (i,j): (164,1), (7991,12518)
X(12656) = X(1)-of-excenters-reflections-triangle
X(12656) = excentral-to-excenters-reflections similarity image of X(164)
X(12656) = orthologic center of these triangles: excenters-reflections to 2nd midarc
The reciprocal orthologic center of these triangles is X(21).
X(12657) lies on these lines: {1,6597}, {145,12543}, {3679,12623}, {3680,10266}, {6599,10950}, {7991,12519}, {11518,12444}, {11519,12451}, {11520,12540}, {11521,12557}, {11522,12615}, {11523,12695}, {11525,12267}, {11530,12639}, {11682,12535}, {12409,12653}
X(12657) = midpoint of X(145) and X(12543)
X(12657) = reflection of X(i) in X(j) for these (i,j): (7991,12519), (12660,1)
The reciprocal orthologic center of these triangles is X(3555).
X(12658) lies on these lines: {1,12521}, {2,9804}, {9,3295}, {40,3555}, {57,12439}, {63,12533}, {145,8726}, {165,8001}, {191,9898}, {200,3646}, {942,2136}, {962,1490}, {1697,5920}, {1698,12620}, {1699,12612}, {1764,12552}, {2951,6361}, {3174,5542}, {3339,5083}, {5531,11379}, {8580,9953}, {9776,9874}
X(12658) = midpoint of X(12533) and X(12537)
X(12658) = reflection of X(i) in X(j) for these (i,j): (1,12521), (7160,12631), (8001,12516), (12654,1)
X(12658) = complement of X(9804)
X(12658) = Ursa-minor-to-excentral similarity image of X(17639)
The reciprocal orthologic center of these triangles is X(3555).
X(12659) lies on these lines: {1,12522}, {2,12542}, {9,12693}, {40,1739}, {57,12442}, {63,12534}, {165,12517}, {1698,12621}, {1699,12613}, {1731,1766}, {1764,12553}, {5709,6361}, {8580,12449}
X(12659) = midpoint of X(12534) and X(12538)
X(12659) = reflection of X(i) in X(j) for these (i,j): (1,12522), (12655,1)
X(12659) = complement of X(12542)
The reciprocal orthologic center of these triangles is X(21).
X(12660) lies on these lines: {1,6597}, {2,12543}, {5,6599}, {9,10266}, {57,12444}, {63,12535}, {165,12519}, {191,12409}, {1698,12623}, {1699,12615}, {1764,12557}, {2949,6907}, {2950,10942}, {3646,12267}, {3871,6595}, {5506,7483}, {6326,6906}, {8580,12451}
X(12660) = midpoint of X(12535) and X(12540)
X(12660) = reflection of X(i) in X(j) for these (i,j): (1,12524), (10266,12639), (12657,1)
X(12660) = complement of X(12543)
The reciprocal orthologic center of these triangles is X(10112).
X(12661) lies on the extangents circle and these lines: {19,113}, {40,12407}, {55,2931}, {65,5504}, {71,265}, {74,3101}, {110,6197}, {125,8251}, {146,9536}, {2550,12319}, {2948,9572}, {3448,9537}, {5584,12302}, {5663,6254}, {6699,10319}, {8539,12596}, {9573,9904}, {10306,12310}, {10636,10663}, {10637,10664}, {11406,12168}, {11428,12228}, {11445,12273}, {11460,12284}, {11471,12295}
X(12661) = reflection of X(10119) in X(8141)
X(12661) = antipode of X(10119) in extangents circle
X(12661) = X(104)-of-extangents-triangle if ABC is acute
X(12661) = orthic-to-extangents similarity image of X(113)
The reciprocal orthologic center of these triangles is X(3).
X(12662) lies on these lines: {19,487}, {40,9906}, {486,10319}, {642,9816}, {2550,12320}, {3101,12221}, {3564,12663}, {5584,12303}, {8251,12601}, {8539,12597}, {10306,12311}, {11406,12169}, {11428,12229}, {11435,12237}, {11445,12274}, {11460,12285}, {11471,12296}
X(12662) = reflection of X(12910) in X(12978)
X(12662) = orthic-to-extangents similarity image of X(487)
The reciprocal orthologic center of these triangles is X(3).
X(12663) lies on these lines: {19,488}, {40,9907}, {485,10319}, {641,9816}, {2550,12321}, {3101,12222}, {3564,12662}, {5584,12304}, {8251,12602}, {8539,12598}, {10306,12312}, {11406,12170}, {11428,12230}, {11435,12238}, {11445,12275}, {11460,12286}, {11471,12297}
X(12663) = reflection of X(12911) in X(12979)
X(12663) = orthic-to-extangents similarity image of X(488)
Let A'B'C' be the orthic triangle. X(12664) is the radical center of the Bevan circles of triangles AB'C', BC'A', CA'B'. (Randy Hutson, July 31 2018)
The reciprocal orthologic center of these triangles is X(72).
X(12664) lies on these lines: {2,9942}, {3,9}, {4,65}, {19,9786}, {33,1498}, {46,1750}, {64,1753}, {72,515}, {185,1824}, {210,11500}, {329,6836}, {388,3427}, {389,1871}, {405,6261}, {442,5927}, {517,5924}, {518,5758}, {912,5787}, {942,5715}, {946,5728}, {950,12672}, {960,6987}, {999,12687}, {1012,10393}, {1064,10396}, {1158,7580}, {1478,12677}, {1532,10395}, {1699,10399}, {1708,3149}, {1709,11507}, {1848,12233}, {1861,6247}, {1872,6000}, {1890,11745}, {2261,11425}, {2646,12114}, {2800,12690}, {2829,12691}, {2900,10306}, {3059,5759}, {3487,8581}, {3488,9848}, {3651,5918}, {3812,6843}, {4185,12136}, {4199,12683}, {5658,6889}, {5794,12667}, {5811,12666}, {5842,7957}, {6259,6917}, {6705,7483}, {6847,10391}, {6908,9943}, {6910,11220}, {6934,12246}, {7971,9856}, {8079,8095}, {8080,8096}, {8226,12608}, {8232,12669}, {8233,12681}, {10445,10974}, {10888,12547}, {11523,12650}
X(12664) = midpoint of X(9799) and X(12528)
X(12664) = reflection of X(i) in X(j) for these (i,j): (1490,5777), (7971,9856), (9960,9942), (12671,3), (12680,12114)
X(12664) = anticomplement of X(9942)
X(12664) = complement of X(9960)
X(12664) = X(68)-of-2nd-extouch-triangle
X(12664) = excentral-to-2nd-extouch similarity image of X(1490)
X(12664) = 2nd-extouch-isotomic conjugate of X(12689)
X(12664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (389,1871,2262), (1864,12688,4), (6260,12616,442)
The reciprocal orthologic center of these triangles is X(12666).
X(12665) lies on the Mandart hyperbola and these lines: {8,153}, {9,48}, {11,5777}, {40,12059}, {72,2829}, {100,1158}, {119,912}, {200,2950}, {518,1537}, {952,1898}, {971,6068}, {1145,6001}, {1388,6265}, {1768,10270}, {1858,10956}, {2802,5881}, {3086,5083}, {3419,12761}, {3711,12515}, {3811,12775}, {5217,12738}, {5534,10087}, {5587,12736}, {5660,5770}, {5720,10090}, {5854,12672}, {6797,9947}, {7330,10058}
X(12665) = midpoint of X(i) and X(j) for these {i,j}: {100,12528}, {153,12532}, {5693,12751}
X(12665) = reflection of X(i) in X(j) for these (i,j): (40,14740), (11,5777), (6797,9947), (11570,119), (12757,6326), (12758,5887)
X(12665) = antipode of X(40) in the Mandart hyperbola
The reciprocal orthologic center of these triangles is X(12665).
X(12666) lies on the Feuerbach hyperbola of the inner Garcia triangle and on these lines: {8,6001}, {40,12059}, {84,997}, {90,104}, {165,191}, {515,5697}, {971,5698}, {1737,6260}, {1898,5768}, {2771,6259}, {2800,3632}, {2801,7971}, {2829,3869}, {3062,12650}, {3419,12676}, {3811,12686}, {5693,6737}, {5811,12664}, {6256,10573}, {9961,11500}, {12688,12701}
X(12666) = reflection of X(9961) in X(11500)
X(12665) = antipode of X(9) in the Mandart hyperbola
X(12665) = extouch-isogonal conjugate of X(13528)
The reciprocal orthologic center of these triangles is X(40).
X(12667) lies on these lines: {1,4}, {2,12114}, {3,1603}, {7,7686}, {8,6001}, {10,84}, {12,6847}, {20,100}, {30,10306}, {36,6927}, {40,2123}, {46,2096}, {56,6848}, {65,12678}, {72,12677}, {80,10305}, {104,6834}, {119,6891}, {149,12761}, {354,5804}, {355,971}, {376,6796}, {377,9799}, {443,5587}, {498,6935}, {499,6969}, {517,6259}, {519,7971}, {631,5251}, {938,12675}, {958,6908}, {960,5811}, {962,3885}, {993,6988}, {1012,3085}, {1125,6939}, {1158,5657}, {1329,6926}, {1385,6893}, {1466,7354}, {1498,9370}, {1512,1788}, {1532,3086}, {1538,11373}, {1698,6705}, {1709,10039}, {1737,10085}, {1837,5768}, {2478,5731}, {2800,5904}, {2975,6838}, {3057,12679}, {3146,5842}, {3149,4293}, {3189,5534}, {3333,7682}, {3419,12777}, {3529,5537}, {3576,5084}, {3577,3671}, {3616,6957}, {3679,7992}, {3822,6855}, {4297,6700}, {5080,6836}, {5082,5881}, {5086,9960}, {5090,12136}, {5176,9961}, {5218,6906}, {5223,11362}, {5234,6684}, {5252,12688}, {5253,6953}, {5261,7680}, {5274,10893}, {5552,6909}, {5660,6903}, {5687,12330}, {5688,6257}, {5689,6258}, {5787,6826}, {5790,12684}, {5794,12664}, {5818,6897}, {6831,10590}, {6833,10588}, {6844,10895}, {6845,10599}, {6851,10526}, {6864,9843}, {6888,10585}, {6890,11681}, {6928,10742}, {6930,10267}, {6932,10527}, {6938,11491}, {6941,10589}, {6942,12248}, {6944,10269}, {6948,11499}, {6956,7951}, {7373,7956}, {7501,8185}, {7966,12575}, {8193,9910}, {8197,12456}, {8204,12457}, {8727,9654}, {9857,12496}, {10431,11015}, {10791,12196}, {10902,11111}, {10914,12676}, {10915,12686}, {10916,12687}, {11900,12668}
X(12667) = reflection of X(i) in X(j) for these (i,j): (1,6260), (4,6256), (20,11500), (84,10), (149,12761), (944,6261), (3189,5534), (6851,10526), (10864,6245), (12246,1158), (12650,946), (12680,9942)
X(12667) = anticomplement of X(12114)
X(12667) = X(84)-of-outer-Garcia-triangle
X(12667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,944,497), (4,1056,946), (4,7967,10531), (4,10805,5603), (4,12115,388), (4,12116,5225), (20,153,3436), (20,7080,10310), (104,6834,7288), (355,6850,2550), (944,5658,6261), (1478,5691,4), (1478,10572,10629), (1837,12680,5768), (5587,10864,6245), (5657,12246,1158), (6906,10786,5218), (6941,10785,10589), (10572,10629,497)
The reciprocal orthologic center of these triangles is X(40).
X(12668) lies on these lines: {30,1490}, {84,402}, {515,12626}, {971,11251}, {1650,6260}, {1709,11912}, {2829,12729}, {6001,12438}, {6245,11897}, {6257,11902}, {6258,11901}, {7971,11910}, {7992,11852}, {9910,11853}, {10085,11913}, {11831,12114}, {11832,12136}, {11839,12196}, {11845,12246}, {11848,12330}, {11885,12496}, {11900,12667}, {11903,12676}, {11904,12677}, {11905,12678}, {11906,12679}, {11909,12680}, {11911,12684}, {11914,12686}, {11915,12687}
X(12668) = reflection of X(i) in X(j) for these (i,j): (84,402), (1650,6260)
X(12668) = X(84)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(72).
X(12669) lies on these lines: {4,7}, {9,6986}, {20,518}, {21,10085}, {63,100}, {84,1803}, {142,6991}, {390,6001}, {515,7672}, {516,3868}, {517,12630}, {912,5759}, {946,11025}, {1158,7676}, {1445,1490}, {2800,7673}, {2829,12755}, {3059,9943}, {3475,8581}, {3873,10431}, {4197,7705}, {4326,7992}, {5273,10167}, {5542,11020}, {5572,11036}, {5779,6883}, {5817,6887}, {5851,9964}, {6261,7677}, {6839,12678}, {7671,11372}, {7678,12608}, {7679,12616}, {8095,8387}, {8096,8388}, {8232,12664}, {8236,12672}, {8237,12681}, {8238,12683}, {8389,12685}, {8732,9942}, {9948,10865}, {10429,11037}, {10889,12547}, {11038,12675}, {11526,12650}
X(12669) = reflection of X(i) in X(j) for these (i,j): (3059,9943), (12528,9), (12688,5572)
X(12669) = X(68)-of-Honsberger-triangle
X(12669) = excentral-to-Honsberger similarity image of X(1490)
X(12669) = Honsberger-isotomic conjugate of X(12718)
he reciprocal orthologic center of these triangles is X(12671).
X(12670) lies on these lines: {8,6835}, {9,3295}, {40,12671}, {1482,12654}, {3057,5920}, {3870,12260}, {8000,9623}
X(12670) = midpoint of X(i) and X(j) for these {i,j}: {9874,12533}, {12756,12777}
The reciprocal orthologic center of these triangles is X(12670).
X(12671) lies on these lines: {1,10045}, {3,9}, {4,9942}, {7,12675}, {20,3869}, {40,12670}, {63,11500}, {65,515}, {210,6796}, {377,9799}, {442,6245}, {1012,2646}, {1158,5918}, {1864,3149}, {2096,6934}, {4304,12672}, {5658,6833}, {5715,11018}, {5787,6917}, {5794,6916}, {5882,9850}, {5927,7483}, {6260,6831}, {7675,11496}, {7682,9844}, {10884,12114}
X(12671) = midpoint of X(20) and X(9960)
X(12671) = reflection of X(i) in X(j) for these (i,j): (4,9942), (12664,3), (12688,6261)
The reciprocal orthologic center of these triangles is X(72).
X(12672) lies on these lines: {1,84}, {3,392}, {4,8}, {5,1519}, {10,1532}, {11,65}, {12,12608}, {20,3877}, {40,936}, {55,6261}, {56,1158}, {78,10306}, {104,1476}, {145,12528}, {210,11362}, {354,5884}, {388,12676}, {390,944}, {474,3359}, {515,3057}, {516,3878}, {518,5693}, {758,4301}, {912,1482}, {942,5603}, {950,12664}, {956,7330}, {997,10310}, {1058,5768}, {1064,3931}, {1108,1765}, {1156,1389}, {1319,5450}, {1385,1621}, {1478,10043}, {1479,10051}, {1490,1697}, {1512,3697}, {1538,4002}, {1737,7681}, {1766,5782}, {1768,5563}, {1858,2099}, {1898,10950}, {2057,5687}, {2096,3600}, {2771,7984}, {2778,12371}, {2801,3244}, {2829,12758}, {2943,5293}, {3337,12767}, {3428,12514}, {3556,10829}, {3576,9943}, {3579,6905}, {3585,10057}, {3601,9942}, {3616,6935}, {3656,11240}, {3698,10175}, {3742,9624}, {3754,3817}, {3812,8227}, {3827,12586}, {3873,5734}, {3880,5881}, {3884,4297}, {3890,5731}, {3899,9589}, {3913,12703}, {3916,11249}, {3927,8158}, {3987,5400}, {4004,6830}, {4018,8727}, {4304,12671}, {4313,9960}, {4342,9949}, {4640,11012}, {4848,7682}, {5044,5657}, {5045,10595}, {5119,11500}, {5252,6256}, {5439,5886}, {5440,11248}, {5554,6957}, {5587,5836}, {5691,5697}, {5692,7991}, {5722,10531}, {5780,12702}, {5787,10936}, {5806,6844}, {5818,10157}, {5854,12665}, {5882,5919}, {5901,10202}, {5902,11522}, {5904,11531}, {6245,12053}, {6259,10935}, {6265,12775}, {6949,11231}, {6952,11230}, {6956,10584}, {6969,9780}, {7373,10569}, {7680,10523}, {7701,11260}, {7962,12650}, {8095,8241}, {8096,8242}, {8236,12669}, {8239,12681}, {8240,12683}, {9785,9799}, {9948,10866}, {10366,11254}, {10947,12701}, {11924,12685}
X(12672) = midpoint of X(i) and X(j) for these {i,j}: {145,12528}, {962,3869}, {3057,12688}, {5691,5697}, {5693,7982}, {5904,11531}
X(12672) = reflection of X(i) in X(j) for these (i,j): (4,9856), (8,5777), (40,960), (65,946), (72,5887), (944,9957), (3555,1482), (4297,3884), (10914,355), (12680,5882), (12711,11496)
X(12672) = anticomplement of X(31788)
X(12672) = X(68)-of-Hutson-intouch-triangle
X(12672) = X(12118)-of-intouch-triangle
X(12672) = excentral-to-Hutson-intouch similarity image of X(1490)
X(12672) = Hutson-intouch-isotomic conjugate of X(12721)
X(12672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1709,12114), (1,1777,1455), (1,12705,1012), (355,12699,10525), (355,12700,3434), (946,12616,11), (962,3434,12700), (1538,9956,6941), (3890,9961,5731), (5603,10785,11373), (5919,12680,5882), (5927,10914,355)
The reciprocal orthologic center of these triangles is X(72).
X(12673) lies on these lines: {84,266}, {363,1490}, {515,9805}, {946,11026}, {971,12488}, {1071,8113}, {1158,8107}, {6001,9836}, {6261,8109}, {6732,8096}, {7992,8140}, {8377,12608}, {8380,12616}, {9783,9799}, {9942,11854}, {9948,11856}, {9960,11886}, {11685,12528}, {11892,12547}
X(12673) = reflection of X(12674) in X(7992)
X(12673) = X(68)-of-inner-Hutson-triangle
X(12673) = excentral-to-inner-Hutson similarity image of X(1490)
X(12673) = inner-Hutson-isotomic conjugate of X(12719)
The reciprocal orthologic center of these triangles is X(72).
X(12674) lies on these lines: {4,8372}, {84,7590}, {168,1490}, {515,9806}, {946,11027}, {971,12489}, {1071,8114}, {1158,8108}, {6001,9837}, {6261,8110}, {7992,8140}, {8378,12608}, {8381,12616}, {9787,9799}, {9942,11855}, {9948,11857}, {9960,11887}, {11686,12528}, {11893,12547}
X(12674) = reflection of X(12673) in X(7992)
X(12674) = X(68)-of-outer-Hutson-triangle
X(12674) = excentral-to-outer-Hutson similarity image of X(1490)
X(12674) = outer-Hutson-isotomic conjugate of X(12720)
The reciprocal orthologic center of these triangles is X(72).
X(12675) lies on these lines: {1,84}, {3,518}, {4,354}, {5,3742}, {7,12671}, {10,9940}, {20,3873}, {40,3555}, {48,9119}, {52,9037}, {57,11500}, {65,944}, {72,3576}, {104,943}, {140,3740}, {210,631}, {355,3812}, {375,11695}, {376,7957}, {388,5768}, {389,8679}, {392,5693}, {442,12757}, {495,12616}, {496,12608}, {515,942}, {516,3881}, {517,550}, {601,3744}, {602,4641}, {774,4322}, {912,960}, {938,12667}, {946,971}, {950,2829}, {952,5836}, {962,3889}, {999,6261}, {1001,7330}, {1056,9850}, {1125,2801}, {1155,11491}, {1158,3295}, {1279,3073}, {1319,1858}, {1376,5534}, {1458,7138}, {1478,11045}, {1479,11046}, {1490,3333}, {1656,3848}, {1768,3746}, {1836,11048}, {1837,11047}, {1864,3086}, {1898,11376}, {2096,4294}, {2771,5609}, {2800,9957}, {2810,9729}, {3057,4305}, {3149,3338}, {3158,10270}, {3243,6769}, {3359,3913}, {3428,10884}, {3475,6847}, {3487,8581}, {3522,4430}, {3523,3681}, {3579,10178}, {3616,12528}, {3753,5881}, {3868,5731}, {3870,10310}, {3892,4301}, {3916,10902}, {3928,10268}, {4292,5173}, {4640,10267}, {4719,5396}, {5044,10165}, {5049,9856}, {5123,10942}, {5252,10805}, {5290,10894}, {5302,6883}, {5439,5587}, {5570,10572}, {5603,12688}, {5691,11034}, {5722,6256}, {5887,10246}, {5904,7987}, {5918,6361}, {5927,8227}, {6245,7680}, {6260,7681}, {6684,11227}, {6907,10916}, {7580,12704}, {7966,7991}, {8550,9004}, {9047,10625}, {9799,11020}, {9844,10893}, {9845,11529}, {9947,10175}, {9948,11035}, {9956,10265}, {9960,11036}, {10531,12679}, {10569,10864}, {10785,11375}, {10806,12701}, {11038,12669}, {11042,12681}, {11043,12683}, {12564,12577}
X(12675) = midpoint of X(i) and X(j) for these {i,j}: {4,12680}, {40,3555}, {65,944}, {3874,4297}, {5882,5884}
X(12675) = reflection of X(i) in X(j) for these (i,j): (10,9940), (355,3812), (942,12005), (946,5045), (960,1385), (5777,1125), (7680,11018), (7686,942)
X(12675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,84,11496), (1,10085,1012), (1,10391,12710), (354,12680,4), (355,10202,3812), (3243,9841,6769), (3555,10167,40), (3889,11220,962), (6260,11019,7681), (9845,11529,12650)
X(12675) = X(68)-of-incircle-circles-triangle
X(12675) = excentral-to-incircle-circles similarity image of X(1490)
X(12675) = incircle-circles-isotomic conjugate of X(12722)
The reciprocal orthologic center of these triangles is X(40).
X(12676) lies on these lines: {4,10309}, {11,84}, {12,12686}, {355,5836}, {388,12672}, {515,10912}, {946,999}, {971,10525}, {1158,1329}, {1376,6260}, {1490,11826}, {1709,9612}, {2829,12699}, {3419,12666}, {5880,12616}, {6245,10893}, {6257,10920}, {6258,10919}, {7704,10785}, {7971,10944}, {7992,10826}, {9910,10829}, {10085,10948}, {10794,12196}, {10871,12496}, {10914,12667}, {10947,12680}, {10949,12687}, {11390,12136}, {11865,12456}, {11866,12457}, {11903,12668}, {11928,12684}
X(12676) = midpoint of X(4) and X(10309)
X(12676) = X(84)-of-inner-Johnson-triangle
X(12676) = reflection of X(i) in X(j) for these (i,j): (12330,6260), (12677,6259)
The reciprocal orthologic center of these triangles is X(40).
X(12677) lies on these lines: {4,5173}, {11,12687}, {12,84}, {72,12667}, {355,5836}, {515,5812}, {958,6260}, {971,10526}, {1478,12664}, {1490,11827}, {1709,10954}, {2829,12738}, {5080,9960}, {6244,11500}, {6245,10894}, {6257,10922}, {6258,10921}, {7971,10950}, {7992,10827}, {9910,10830}, {10085,10523}, {10786,12246}, {10795,12196}, {10872,12496}, {10953,12680}, {10955,12686}, {11374,12114}, {11391,12136}, {11867,12456}, {11868,12457}, {11904,12668}, {11929,12684}
X(12677) = reflection of X(12676) in X(6259)
X(12677) = X(84)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12678) lies on these lines: {1,6259}, {4,354}, {5,10085}, {12,84}, {56,6260}, {65,12667}, {210,6916}, {495,1709}, {515,1836}, {518,6925}, {944,5048}, {971,1478}, {1155,2096}, {1483,12699}, {1490,7354}, {1538,10072}, {1768,11698}, {2801,3419}, {2829,12739}, {3085,12246}, {3436,9943}, {3576,4679}, {3585,5787}, {3742,6957}, {3877,9809}, {4293,5658}, {4860,7682}, {5080,11220}, {5229,9799}, {5252,6001}, {5534,11826}, {5584,12527}, {5691,11529}, {5794,12528}, {6245,10895}, {6253,9579}, {6257,10924}, {6258,10923}, {6839,12669}, {7971,10944}, {7992,9578}, {8273,12572}, {9612,10864}, {9614,9845}, {9654,12684}, {9910,10831}, {10797,12196}, {10873,12496}, {10956,12686}, {10957,12687}, {11375,12114}, {11376,12608}, {11392,12136}, {11501,12330}, {11869,12456}, {11870,12457}, {11905,12668}
X(12678) = reflection of X(i) in X(j) for these (i,j): (1709,495), (5252,12115)
X(12678) = {X(1), X(6259)}-harmonic conjugate of X(12679)
X(12678) = X(84)-of-1st-Johnson-Yff-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12679) lies on these lines: {1,6259}, {3,4679}, {4,65}, {5,1709}, {11,84}, {12,12705}, {55,6260}, {64,1842}, {79,3062}, {210,5811}, {329,7957}, {480,516}, {496,1699}, {499,1538}, {515,2098}, {946,3304}, {952,3627}, {960,6925}, {962,3880}, {971,1479}, {1012,11375}, {1155,6848}, {1158,1532}, {1456,7952}, {1478,9856}, {1490,6284}, {1519,11376}, {1547,1892}, {1750,5812}, {1854,1877}, {2478,9943}, {2829,12740}, {3057,12667}, {3086,12246}, {3091,5880}, {3146,5057}, {3338,7956}, {3583,5787}, {3683,6908}, {3812,6957}, {3838,6837}, {3868,9809}, {4294,5658}, {4640,6838}, {5046,9961}, {5087,6890}, {5221,7682}, {5225,9799}, {5252,6256}, {5556,10429}, {5584,12572}, {5715,7965}, {5720,11826}, {5881,12700}, {5918,6865}, {6245,7702}, {6257,10926}, {6258,10925}, {7971,10950}, {7992,9581}, {9612,11372}, {9614,10864}, {9669,12684}, {9797,9812}, {9910,10832}, {10531,12675}, {10798,12196}, {10863,12436}, {10874,12496}, {10958,12686}, {10959,12687}, {11113,12520}, {11393,12136}, {11502,12330}, {11871,12456}, {11872,12457}, {11906,12668}
X(12679) = reflection of X(i) in X(j) for these (i,j): (1837,4), (10085,496)
X(12679) = X(84)-of-2nd-Johnson-Yff-triangle
X(12679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,6259,12678), (1699,10085,496)
The reciprocal orthologic center of these triangles is X(40).
X(12680) lies on these lines: {1,971}, {3,210}, {4,354}, {8,9859}, {9,8273}, {10,10167}, {11,6260}, {12,6245}, {20,518}, {33,12136}, {40,5918}, {48,1903}, {55,84}, {56,1490}, {65,515}, {72,2801}, {145,9961}, {185,8679}, {198,963}, {200,9841}, {227,7004}, {355,3698}, {388,9799}, {516,3555}, {517,1657}, {912,3962}, {942,4355}, {944,3057}, {952,3893}, {956,12520}, {958,5784}, {960,5731}, {1040,9370}, {1056,12710}, {1125,5927}, {1155,11500}, {1208,2183}, {1319,1898}, {1385,5259}, {1478,5787}, {1479,6259}, {1697,7992}, {1698,5789}, {1699,5045}, {1709,3295}, {1750,3333}, {1768,3579}, {1837,5768}, {2098,7971}, {2099,12650}, {2310,4322}, {2646,12114}, {2829,12743}, {2951,8001}, {3059,5584}, {3086,5658}, {3091,3742}, {3146,3873}, {3243,12651}, {3303,12705}, {3486,9960}, {3522,3681}, {3523,3740}, {3576,5777}, {3600,10394}, {3624,10157}, {3683,7330}, {3689,5534}, {3697,10164}, {3748,11496}, {3848,5056}, {3889,9812}, {3983,6684}, {4298,5728}, {4430,5059}, {4662,10178}, {4679,5811}, {5044,7987}, {5049,11522}, {5173,9579}, {5290,11018}, {5302,6986}, {5432,6705}, {5572,11037}, {5587,9940}, {5882,5919}, {5889,9037}, {6257,10928}, {6258,10927}, {6744,10569}, {6762,12565}, {6765,10860}, {8580,9858}, {9844,11019}, {9910,10833}, {10106,12711}, {10443,10823}, {10480,12547}, {10544,12721}, {10799,12196}, {10877,12496}, {10947,12676}, {10953,12677}, {10965,12686}, {10966,12687}, {11873,12456}, {11874,12457}, {11909,12668}
X(12680) = midpoint of X(145) and X(9961)
X(12680) = reflection of X(i) in X(j) for these (i,j): (4,12675), (8,9943), (72,4297), (3057,944), (3059,5732), (5691,942), (6253,4292), (7957,20), (9848,9845), (12528,960), (12664,12114), (12667,9942), (12672,5882), (12688,1)
X(12680) = X(84)-of-Mandart-incircle-triangle
X(12680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,12675,354), (8,11220,9943), (944,12246,4294), (3295,12684,1709), (5534,7171,10310), (5534,10310,3689), (5731,12528,960), (5882,12672,5919), (9947,11227,1698)
The reciprocal orthologic center of these triangles is X(72).
X(12681) lies on these lines: {4,7595}, {84,2067}, {515,9808}, {517,12638}, {946,11030}, {971,12490}, {1158,8224}, {1490,8231}, {2800,12744}, {2829,12768}, {6001,7596}, {6245,7683}, {6261,8225}, {7992,8244}, {8095,8247}, {8096,8248}, {8228,12608}, {8230,12616}, {8233,12664}, {8237,12669}, {8239,12672}, {8246,12683}, {9789,9799}, {9942,10858}, {9948,10867}, {9960,10885}, {10891,12547}, {11042,12675}, {11532,12650}, {11687,12528}, {11996,12685}
X(12681) = X(68)-of-2nd-Pamfilos-Zhou-triangle
X(12681) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(1490)
X(12681) = 2nd-Pamfilos-Zhou-isotomic conjugate of X(12724)
The reciprocal orthologic center of these triangles is X(10308).
X(12682) lies on these lines: {8,12535}, {9,10266}, {72,3648}, {1145,11684}, {3337,11263}
X(12682) = midpoint of X(12769) and X(12786)
The reciprocal orthologic center of these triangles is X(72).
X(12683) lies on these lines: {4,240}, {21,84}, {40,12530}, {515,2292}, {517,12642}, {846,1490}, {946,11031}, {971,9959}, {1158,4220}, {2800,12746}, {2829,12770}, {4199,12664}, {4425,6245}, {5051,12616}, {6001,9840}, {7992,8245}, {8095,8249}, {8096,8250}, {8229,12608}, {8238,12669}, {8240,12672}, {8246,12681}, {8425,12685}, {8731,9942}, {9791,9799}, {9948,10868}, {10892,12547}, {11043,12675}, {11533,12650},
X(12683) = X(68)-of-1st-Sharygin-triangle
X(12683) = excentral-to-1st-Sharygin similarity image of X(1490)
X(12683) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13256)
X(12683) = 1st-Sharygin-isotomic conjugate of X(12725)
{11688,12528}
The reciprocal orthologic center of these triangles is X(40).
X(12684) lies on these lines: {3,9}, {4,5708}, {20,3927}, {30,9799}, {140,5658}, {355,9948}, {381,6245}, {382,2095}, {405,11220}, {515,1657}, {517,7992}, {944,10386}, {952,12632}, {956,9961}, {999,10085}, {1156,5265}, {1482,6001}, {1598,12136}, {1656,6260}, {1709,3295}, {2829,12747}, {3062,3333}, {3146,12690}, {3526,6705}, {3560,9960}, {3940,12528}, {5045,11372}, {5220,12512}, {5558,5603}, {5758,5843}, {5789,6907}, {5790,12667}, {6257,11917}, {6258,11916}, {6767,12705}, {7373,9856}, {7517,9910}, {7971,10247}, {8148,12650}, {9301,12496}, {9654,12678}, {9669,12679}, {9708,9943}, {10167,11108}, {10246,12114}, {10679,12631}, {11842,12196}, {11849,12330}, {11875,12456}, {11876,12457}, {11911,12668}, {11928,12676}, {11929,12677}, {12000,12686}, {12001,12687}
X(12684) = midpoint of X(i) and X(j) for these {i,j}: {7992,10864}, {9799,12246}
X(12684) = reflection of X(i) in X(j) for these (i,j): (3,84), (355,9948), (382,5787), (6259,6245), (8148,12650)
X(12684) = X(84)-of-X3-ABC-reflections-triangle
X(12684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1709,12680,3295), (5044,9841,3), (5777,7171,3), (6245,6259,381), (10085,12688,999)
The reciprocal orthologic center of these triangles is X(72).
X(12685) lies on these lines: {515,12445}, {517,12646}, {912,8130}, {946,8083}, {971,12491}, {2800,12748}, {2829,12774}, {6001,8351}, {6261,7587}, {7992,8423}, {8126,12528}, {8382,12616}, {8389,12669}, {8425,12683}, {8729,9942}, {9799,11891}, {9948,11860}, {9960,11890}, {10502,12688}, {11033,12005}, {11535,12650}, {11896,12547}, {11924,12672}, {11996,12681}
X(12685) = X(68)-of-Yff-central-triangle
X(12685) = excentral-to-Yff-central similarity image of X(1490)
X(12685) = Yff-central-isotomic conjugate of X(12728)
The reciprocal orthologic center of these triangles is X(40).
X(12686) lies on these lines: {1,84}, {2,1158}, {9,119}, {12,12676}, {40,3436}, {46,1532}, {57,1519}, {515,3895}, {971,10679}, {1490,11248}, {1697,6938}, {1706,6923}, {2077,10860}, {2829,5119}, {3085,10309}, {3358,10202}, {3811,12666}, {4640,10270}, {5552,6260}, {6245,10531}, {6257,10930}, {6258,10929}, {6259,10942}, {6261,6909}, {6916,12514}, {6957,12616}, {7330,9623}, {9910,10834}, {10803,12196}, {10805,12246}, {10878,12496}, {10915,12667}, {10955,12677}, {10956,12678}, {10958,12679}, {10965,12680}, {11400,12136}, {11509,12330}, {11881,12456}, {11882,12457}, {11914,12668}, {12000,12684}
X(12686) = reflection of X(84) in X(1709)
X(12686) = X(84)-of-inner-Yff-tangents-triangle
X(12686) = {X(84),X(7971)}-harmonic conjugate of X(12687)
The reciprocal orthologic center of these triangles is X(40).
X(12687) lies on these lines: {1,84}, {11,12677}, {496,5715}, {515,12649}, {952,5709}, {956,9942}, {971,10680}, {999,12664}, {1158,5731}, {1490,11249}, {2829,12750}, {2975,6261}, {6245,10532}, {6257,10932}, {6258,10931}, {6259,10943}, {6260,10527}, {9910,10835}, {10804,12196}, {10806,12246}, {10879,12496}, {10916,12667}, {10949,12676}, {10957,12678}, {10959,12679}, {10966,12680}, {11401,12136}, {11510,12330}, {11883,12456}, {11884,12457}, {11915,12668}, {12001,12684}
X(12687) = reflection of X(84) in X(10085)
X(12687) = X(84)-of-outer-Yff-tangents-triangle
X(12687) = {X(84),X(7971)}-harmonic conjugate of X(12686)
The reciprocal orthologic center of these triangles is X(65).
X(12688) lies on these lines: {1,971}, {2,9943}, {3,1709}, {4,65}, {7,10429}, {9,5584}, {10,5927}, {11,6245}, {12,6260}, {19,64}, {20,960}, {28,12262}, {30,5887}, {33,221}, {34,1854}, {37,4300}, {40,210}, {55,1490}, {56,84}, {57,7992}, {72,516}, {104,10308}, {142,7958}, {165,5044}, {185,1839}, {207,7008}, {226,12711}, {227,2635}, {241,1044}, {329,9800}, {354,946}, {382,517}, {392,4297}, {405,12520}, {411,4640}, {442,12617}, {497,9799}, {515,3057}, {518,962}, {774,1427}, {912,12699}, {936,10860}, {942,1699}, {944,5919}, {950,12709}, {991,6051}, {999,10085}, {1001,10884}, {1012,2646}, {1042,2310}, {1125,10167}, {1155,1158}, {1192,5338}, {1204,2355}, {1210,9948}, {1319,12114}, {1385,5426}, {1425,1547}, {1478,6259}, {1479,5787}, {1532,12616}, {1538,7741}, {1593,2182}, {1698,10157}, {1824,11381}, {1829,5895}, {1848,2883}, {1871,6000}, {1872,2818}, {1902,3827}, {2098,12650}, {2099,7971}, {2264,5776}, {2771,7728}, {2777,10693}, {2778,10721}, {2801,3555}, {3085,5658}, {3091,3812}, {3146,3869}, {3427,10309}, {3428,7330}, {3485,9960}, {3487,12710}, {3523,10178}, {3616,11220}, {3624,11227}, {3646,10857}, {3671,5728}, {3678,5493}, {3679,9947}, {3689,10306}, {3698,5587}, {3817,5439}, {3838,6828}, {3868,9812}, {3876,9778}, {3983,5657}, {4005,6361}, {4199,12713}, {4293,12246}, {4423,8726}, {4679,6865}, {4731,5818}, {4882,9954}, {5045,11522}, {5057,6895}, {5087,6943}, {5247,9355}, {5252,12667}, {5433,6705}, {5572,11036}, {5603,12675}, {5720,10310}, {5732,8273}, {5794,6925}, {5806,5902}, {5880,6835}, {5883,12571}, {5934,12707}, {5935,12708}, {6738,9844}, {6831,12608}, {6847,9942}, {7580,12514}, {7701,11012}, {8079,12714}, {8226,12609}, {8227,9940}, {8232,12706}, {8233,12712}, {8582,9842}, {8583,9841}, {8727,12047}, {9843,10863}, {9955,10202}, {10176,12512}, {10431,11415}, {10445,10822}, {10473,12547}, {10477,12544}, {10502,12685}, {10888,12548}, {11263,12558}, {11406,12335}, {11509,12330}, {11523,12651}, {12666,12701}
X(12688) = midpoint of X(i) and X(j) for these {i,j}: {962,12528}, {3146,3869}, {5904,9589}, {9800,12529}
X(12688) = reflection of X(i) in X(j) for these (i,j): (1,9856), (20,960), (40,5777), (65,4), (3057,12672), (3555,4301), (3893,5881), (3962,5693), (5493,3678), (7957,72), (9961,9943), (12669,5572), (12671,6261), (12680,1)
X(12688) = anticomplement of X(9943)
X(12688) = complement of X(9961)
X(12688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,9961,9943), (9,12565,5584), (40,5777,210), (65,1898,1864), (999,12684,10085), (1012,6261,2646), (1158,3149,1155), (1490,12705,55), (1836,1858,65), (3649,7965,946), (8581,9848,1), (9850,10866,1)
X(12688) = excentral-to-2nd-extouch similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12689) lies on these lines: {2,9944}, {4,75}, {9,1721}, {72,516}, {226,12723}, {307,1827}, {329,9801}, {405,990}, {442,12618}, {950,12721}, {971,10444}, {1490,12717}, {1750,7996}, {1766,3693}, {3487,12722}, {3663,5728}, {4199,12725}, {5927,9950}, {5934,12719}, {5935,12720}, {8079,12726}, {8226,12610}, {8232,12718}, {8233,12724}, {10888,12549}, {11523,12652}
X(12689) = midpoint of X(9801) and X(12530)
X(12689) = reflection of X(9962) in X(9944)
X(12689) = anticomplement of X(9944)
X(12689) = complement of X(9962)
X(12689) = X(317)-of-2nd-extouch-triangle
X(12689) = excentral-to-2nd-extouch similarity image of X(1721)
X(12689) = 2nd-extouch-isogonal conjugate of X(5928)
X(12689) = 2nd-extouch-isotomic conjugate of X(12664)
X(12689) = anticomplement, wrt 2nd extouch triangle, of X(10445)
X(12689) = {X(2), X(9962)}-harmonic conjugate of X(9944)
The reciprocal orthologic center of these triangles is X(8).
X(12690) lies on these lines: {2,9945}, {4,145}, {8,4756}, {9,80}, {10,6154}, {11,214}, {30,3218}, {72,2802}, {100,405}, {104,7580}, {119,8226}, {140,11015}, {226,1317}, {329,9802}, {355,3895}, {382,12649}, {517,12691}, {900,4707}, {1387,3488}, {1479,5289}, {1484,6907}, {1490,6264}, {1750,7993}, {2320,11680}, {2475,12433}, {2800,12664}, {2829,10864}, {3065,6598}, {3146,12684}, {3306,5722}, {3487,12735}, {3583,4867}, {3627,3868}, {3830,5905}, {4199,12746}, {4746,12572}, {4999,5441}, {5225,5730}, {5436,6667}, {5728,12736}, {5790,6976}, {5840,12515}, {5854,9897}, {5927,9951}, {5934,12733}, {5935,12734}, {6174,6702}, {6913,12331}, {7972,9612}, {8079,8097}, {8080,8098}, {8232,12730}, {8233,12744}, {9024,10477}, {9803,10724}, {10888,12550}, {10993,12619}, {11523,12653}
X(12690) = midpoint of X(i) and X(j) for these {i,j}: {9802,12531}, {9803,10724}
X(12690) = reflection of X(i) in X(j) for these (i,j): (100,12019), (1145,80), (1537,10738), (5541,3036), (6154,10), (6224,1387), (9963,9945), (10609,11), (10993,12619), (12732,1145)
X(12690) = anticomplement of X(9945)
X(12690) = complement of X(9963)
X(12690) = X(74)-of-2nd-extouch-triangle
X(12690) = excentral-to-2nd-extouch similarity image of X(5541)
X(12690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,9963,9945), (80,5541,3036), (3036,5541,1145), (3419,3586,11113), (6224,10707,1387)
The reciprocal orthologic center of these triangles is X(3869).
X(12691) lies on these lines: {2,9946}, {4,80}, {9,48}, {72,952}, {119,125}, {149,5758}, {226,8068}, {329,9803}, {404,5720}, {405,6265}, {517,12690}, {908,912}, {944,5692}, {950,12758}, {1387,5728}, {1490,1768}, {1512,6001}, {1708,10090}, {1750,12767}, {2802,12625}, {2829,12664}, {3487,5083}, {3651,12695}, {3678,11491}, {3754,5587}, {4199,12770}, {5884,7951}, {5904,12116}, {5927,9952}, {5934,12759}, {5935,12760}, {6224,6987}, {6264,11523}, {6702,6829}, {7580,12515}, {8000,10698}, {8079,12771}, {8226,12611}, {8232,12755}, {8233,12768}, {9612,11571}, {10058,10393}, {10888,12551}
X(12691) = midpoint of X(9803) and X(12532)
X(12691) = reflection of X(i) in X(j) for these (i,j): (9964,9946), (11570,10265), (12757,214)
X(12691) = anticomplement of X(9946)
X(12691) = complement of X(9964)
The reciprocal orthologic center of these triangles is X(3555).
X(12692) lies on these lines: {2,12439}, {4,4863}, {9,3295}, {210,12260}, {329,9804}, {405,12521}, {442,3555}, {518,12777}, {950,5920}, {1750,8001}, {3085,3983}, {5927,9953}, {7580,12516}, {8226,12612}, {10888,12552}, {11523,12654}
X(12692) = midpoint of X(9804) and X(12533)
X(12692) = reflection of X(12537) in X(12439)
X(12692) = anticomplement of X(12439)
X(12692) = complement of X(12537)
The reciprocal orthologic center of these triangles is X(3555).
X(12693) lies on these lines: {2,12442}, {4,4723}, {9,12659}, {329,12534}, {405,12522}, {442,12621}, {2325,10445}, {5927,12449}, {7580,12517}, {8226,12613}, {10888,12553}, {11523,12655}
X(12693) = midpoint of X(12534) and X(12542)
X(12693) = reflection of X(12538) in X(12442)
X(12693) = anticomplement of X(12442)
X(12693) = complement of X(12538)
The reciprocal orthologic center of these triangles is X(1).
X(12694) lies on these lines: {1,8079}, {2,12443}, {9,164}, {167,1750}, {177,226}, {329,9807}, {405,12523}, {442,12622}, {950,8422}, {5571,5728}, {5927,12450}, {7670,8232}, {10888,12554}
X(12694) = midpoint of X(9807) and X(11691)
X(12694) = orthologic center of these triangles: 2nd extouch to 2nd midarc
X(12694) = X(1)-of-2nd-extouch-triangle
X(12694) = excentral-to-2nd-extouch similarity image of X(164)
X(12694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,12539,12443), (8079,8080,1)
The reciprocal orthologic center of these triangles is X(21).
X(12695) lies on these lines: {2,12444}, {4,5535}, {9,10266}, {35,72}, {329,12535}, {405,12524}, {442,1749}, {3065,6598}, {3651,12691}, {3652,12600}, {5927,12451}, {7580,12519}, {8226,12615}, {10888,12557}, {11523,12657}
X(12695) = midpoint of X(12535) and X(12543)
X(12695) = reflection of X(12540) in X(12444)
X(12695) = anticomplement of X(12444)
X(12695) = complement of X(12540)
The reciprocal orthologic center of these triangles is X(4).
X(12696) lies on these lines: {1,30}, {3,11831}, {4,11900}, {10,11897}, {40,402}, {46,11913}, {65,11909}, {515,12626}, {516,12113}, {517,11251}, {946,1650}, {962,4240}, {1902,11832}, {2802,12752}, {5119,11912}, {5812,11904}, {5840,12729}, {6001,12791}, {6361,11845}, {7982,11910}, {7991,11852}, {9911,11853}, {10306,11848}, {11839,12197}, {11863,12458}, {11864,12459}, {11885,12497}, {11901,12697}, {11902,12698}, {11903,12700}, {11911,12702}, {11914,12703}, {11915,12704}
X(12696) = midpoint of X(962) and X(4240)
X(12696) = X(40)-of-Gossard-triangle
X(12696) = reflection of X(i) in X(j) for these (i,j): (40,402), (1650,946), (12438,11251)
The reciprocal orthologic center of these triangles is X(4).
X(12697) lies on these lines: {1,11824}, {3,11370}, {4,5689}, {6,40}, {10,6202}, {46,10048}, {65,10927}, {515,6258}, {516,5871}, {517,1161}, {946,5591}, {962,1271}, {1699,10514}, {1836,10923}, {1902,11388}, {2802,12753}, {5119,10040}, {5589,7991}, {5595,9911}, {5603,10517}, {5605,7982}, {5812,10921}, {5840,6263}, {6001,6267}, {6215,12699}, {6281,9589}, {6361,10783}, {8198,12458}, {8205,12459}, {9994,12497}, {10306,11497}, {10792,12197}, {10919,12700}, {10925,12701}, {10929,12703}, {10931,12704}, {11901,12696}, {11916,12702}
X(12697) = reflection of X(i) in X(j) for these (i,j): (3641,1161), (12698,40)
X(12697) = X(40)-of-inner-Grebe-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12698) lies on these lines: {1,11825}, {3,11371}, {4,5688}, {6,40}, {10,6201}, {46,10049}, {65,10928}, {515,6257}, {516,5870}, {517,1160}, {946,5590}, {962,1270}, {1699,10515}, {1836,10924}, {1902,11389}, {2802,12754}, {5119,10041}, {5588,7991}, {5594,9911}, {5603,10518}, {5604,7982}, {5812,10922}, {5840,6262}, {6001,6266}, {6214,12699}, {6278,9589}, {6361,10784}, {8199,12458}, {8206,12459}, {9995,12497}, {10306,11498}, {10793,12197}, {10920,12700}, {10926,12701}, {10930,12703}, {10932,12704}, {11902,12696}, {11917,12702}
X(12698) = reflection of X(i) in X(j) for these (i,j): (3640,1160), (12697,40)
X(12698) = X(40)-of-outer-Grebe-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12699) lies on these lines: {1,30}, {2,3579}, {3,142}, {4,8}, {5,40}, {7,1058}, {10,381}, {11,46}, {12,5119}, {19,7359}, {20,1385}, {35,11375}, {36,11376}, {52,2807}, {55,6985}, {56,1770}, {57,496}, {63,3650}, {65,1479}, {74,12261}, {80,5560}, {84,3254}, {85,5195}, {100,12611}, {113,12778}, {140,165}, {145,3543}, {146,149}, {219,1839}, {224,1537}, {226,3295}, {238,582}, {320,10446}, {347,10400}, {376,3616}, {377,392}, {382,515}, {388,9957}, {390,3487}, {442,5250}, {484,7741}, {495,1697}, {497,942}, {499,1155}, {519,3830}, {528,3811}, {546,5587}, {548,7987}, {549,3624}, {550,3576}, {551,3534}, {595,3772}, {631,9778}, {908,5687}, {912,12688}, {943,8543}, {944,3146}, {950,9668}, {952,3627}, {999,4292}, {1012,11249}, {1056,9785}, {1159,6738}, {1210,9669}, {1319,4299}, {1320,10728}, {1330,4673}, {1387,1420}, {1478,3057}, {1480,5710}, {1483,12678}, {1484,1768}, {1519,3149}, {1538,6848}, {1539,12368}, {1571,3815}, {1572,5254}, {1596,7713}, {1597,12410}, {1621,3651}, {1656,3817}, {1657,4297}, {1658,9625}, {1702,7583}, {1703,7584}, {1706,3820}, {1709,10943}, {1737,10896}, {1745,5399}, {1750,5534}, {1788,10591}, {1837,3583}, {1892,4318}, {2077,6924}, {2093,9581}, {2095,6245}, {2099,10572}, {2102,10737}, {2103,10736}, {2325,10445}, {2475,3877}, {2478,3753}, {2550,5044}, {2646,4302}, {2775,4010}, {2800,10738}, {2802,10742}, {2809,10741}, {2817,10747}, {2829,12676}, {2886,5791}, {3062,5843}, {3073,5398}, {3086,3474}, {3090,9779}, {3091,5657}, {3120,3915}, {3333,4312}, {3338,4338}, {3340,3586}, {3359,6922}, {3416,3818}, {3428,3560}, {3452,9709}, {3485,4294}, {3524,5550}, {3526,10164}, {3529,5731}, {3545,9780}, {3555,5905}, {3585,5252}, {3587,8728}, {3617,3839}, {3628,7988}, {3634,5055}, {3679,3845}, {3702,6327}, {3832,5818}, {3838,10198}, {3843,4691}, {3847,5955}, {3850,7989}, {3851,10175}, {3853,5844}, {3878,5794}, {3897,12600}, {3916,10527}, {3927,4847}, {3944,5255}, {3966,4647}, {4018,12649}, {4298,7373}, {4512,6675}, {4677,12101}, {4857,5902}, {4863,5904}, {5010,5443}, {5046,7693}, {5070,10171}, {5073,5882}, {5076,12645}, {5079,10172}, {5122,7288}, {5128,10593}, {5221,11238}, {5231,5709}, {5259,7688}, {5271,9958}, {5303,6906}, {5439,6899}, {5530,9554}, {5541,11698}, {5584,6883}, {5708,11019}, {5715,6907}, {5719,10386}, {5720,5763}, {5734,7967}, {5759,6846}, {5762,7330}, {5768,9800}, {5787,5878}, {5806,6827}, {5842,6261}, {6214,12698}, {6215,12697}, {6221,8983}, {6244,6918}, {6260,12631}, {6560,7968}, {6561,7969}, {6583,9961}, {6745,10306}, {6763,7701}, {6767,12575}, {6796,11849}, {6836,10531}, {6842,7680}, {6845,11680}, {6882,7681}, {6911,10310}, {6914,11012}, {6925,10532}, {6928,7686}, {6972,7704}, {7502,9591}, {7530,8185}, {7580,10267}, {7745,9620}, {7951,11010}, {7962,9613}, {7970,10723}, {7978,10733}, {7983,10722}, {7984,10721}, {8193,9818}, {8200,12458}, {8207,12459}, {8725,12264}, {8981,9616}, {9655,10106}, {9708,12572}, {9821,12263}, {9904,10264}, {9943,10202}, {9996,12497}, {10039,10895}, {10167,10596}, {10679,11500}, {10680,12114}, {10695,10727}, {10696,10732}, {10697,10725}, {10698,10724}, {10703,10726}, {10796,12197}, {10915,11236}, {10916,11235}, {10942,12703}, {11529,12433}, {11599,12188}, {11699,12383}, {11720,12121}, {11928,12616}, {12163,12259}
X(12699) = midpoint of X(i) and X(j) for these {i,j}: {4,962}, {40,9589}, {382,1482}, {944,3146}, {1320,10728}, {2102,10737}, {2103,10736}, {5691,7982}, {5812,12700}, {5881,11531}, {7970,10723}, {7978,10733}, {7983,10722}, {7984,10721}, {10695,10727}, {10696,10732}, {10697,10725}, {10698,10724}, {10703,10726}
X(12699) = reflection of X(i) in X(j) for these (i,j): (3,946), (20,1385), (40,5), (74,12261), (100,12611), (145,11278), (355,4), (550,5901), (1482,4301), (1657,4297), (1768,1484), (3359,7956), (3416,3818), (3534,551), (3579,9955), (3654,381), (3655,3656), (3679,3845), (5493,6684), (5541,11698), (5690,546), (5691,3627), (5887,9856), (6265,1537), (6361,3579), (6769,5763), (7991,5690), (8725,12264), (9778,11230), (9821,12263), (9904,10264), (11500,12608), (12121,11720), (12163,12259), (12188,11599), (12368,1539), (12383,11699), (12515,11), (12702,10), (12778,113)
X(12699) = isogonal conjugate of X(10623)
X(12699) = anticomplement of X(3579)
X(12699) = complement of X(6361)
X(12699) = X(40)-of-Johnson-triangle
X(12699) = homothetic center of Ehrmann mid-triangle and outer Garcia triangle
X(12699) = X(12702)-of-Ehrmann-mid-triangle
X(12699) = X(12702)-of-outer-Garcia-triangle
X(12699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,79,10404), (2,6361,3579), (3,946,5886), (4,5758,5777), (7,1058,5045), (10,12702,3654), (20,5603,1385), (40,1699,5), (55,12047,11374), (57,9614,496), (381,12702,10), (962,9812,4), (962,10248,12245), (1699,9589,40), (1836,10404,79), (1836,12701,1), (3058,3649,1), (3434,11415,72), (3579,9955,2), (10165,12512,3)
The reciprocal orthologic center of these triangles is X(4).
X(12700) lies on these lines: {1,11826}, {3,10624}, {4,8}, {5,1706}, {10,10893}, {11,40}, {12,12703}, {30,12650}, {46,10948}, {65,10947}, {78,1537}, {79,11224}, {390,1385}, {474,5886}, {496,3359}, {515,10912}, {516,8666}, {528,6261}, {550,3254}, {946,1376}, {952,3680}, {1058,9940}, {1158,3813}, {1482,10106}, {1519,5687}, {1621,6940}, {1697,6907}, {1709,6763}, {1836,7982}, {2077,11376}, {2802,12761}, {3579,6926}, {3656,11112}, {3753,10531}, {3880,6256}, {3913,12608}, {4002,6898}, {4187,5250}, {4863,5693}, {5048,7702}, {5119,10523}, {5439,10596}, {5603,6904}, {5657,6919}, {5709,10943}, {5840,12737}, {5881,12679}, {6361,10785}, {6850,9957}, {6891,7743}, {6916,9785}, {6964,9955}, {7991,10826}, {9911,10829}, {10167,10806}, {10679,11374}, {10794,12197}, {10871,12497}, {10919,12697}, {10920,12698}, {10949,12704}, {11235,12616}, {11865,12458}, {11866,12459}, {11903,12696}, {11928,12702}
X(12700) = reflection of X(i) in X(j) for these (i,j): (355,10525), (1158,3813), (3913,12608), (5812,12699), (10306,946)
X(12700) = X(40)-of-inner-Johnson-triangle
X(12700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,10914,355), (40,9614,6922), (962,3434,12672), (3434,12672,355)
The reciprocal orthologic center of these triangles is X(4).
X(12701) lies on these lines: {1,30}, {3,11376}, {4,1000}, {5,5119}, {7,5558}, {8,3967}, {10,4679}, {11,40}, {12,1697}, {20,1319}, {21,5832}, {35,5886}, {36,11373}, {46,496}, {55,946}, {56,516}, {57,9589}, {63,3813}, {65,497}, {72,4863}, {78,528}, {145,5057}, {149,3869}, {165,5433}, {210,5082}, {226,3303}, {354,1058}, {355,3583}, {381,10039}, {388,5919}, {390,3485}, {498,9955}, {499,3579}, {515,2098}, {517,1479}, {518,1898}, {546,10827}, {550,1387}, {908,3913}, {944,5048}, {950,2099}, {960,3434}, {999,1770}, {1012,10966}, {1038,12652}, {1125,5217}, {1155,3086}, {1191,3914}, {1210,11238}, {1317,6259}, {1385,4302}, {1388,4297}, {1478,9957}, {1482,9668}, {1512,10893}, {1519,11500}, {1537,6261}, {1698,7173}, {1709,10949}, {1737,9669}, {1788,5183}, {1839,2256}, {1864,5758}, {1902,11393}, {2475,3890}, {2478,5836}, {2646,4294}, {2802,12764}, {2886,5250}, {3146,3476}, {3295,12047}, {3296,5551}, {3304,4292}, {3305,9710}, {3333,11246}, {3416,3702}, {3419,3878}, {3421,3893}, {3436,3880}, {3486,11011}, {3487,3748}, {3586,5812}, {3601,5805}, {3612,5901}, {3616,5880}, {3673,5195}, {3698,5084}, {3746,11374}, {3772,3915}, {3868,5180}, {3876,7673}, {3877,5794}, {3885,5080}, {3895,12607}, {3911,5493}, {4305,10595}, {4342,10106}, {4388,4673}, {4640,10527}, {4857,5722}, {4861,11114}, {4870,5703}, {5087,5552}, {5123,5187}, {5221,11019}, {5432,8227}, {5533,12515}, {5657,10591}, {5690,10826}, {5691,7962}, {5727,11531}, {5840,12740}, {6001,12116}, {6734,11235}, {6949,7704}, {6985,11508}, {7288,9778}, {7580,11510}, {7686,10531}, {7741,11010}, {7991,9581}, {8715,11813}, {8727,10957}, {9578,9819}, {9671,11362}, {9779,10588}, {9911,10832}, {10065,12261}, {10087,12611}, {10306,11502}, {10366,10373}, {10698,12743}, {10738,12758}, {10798,12197}, {10806,12675}, {10874,12497}, {10925,12697}, {10926,12698}, {10947,12672}, {10958,12703}, {10959,12704}, {10965,12608}, {11871,12458}, {11872,12459}, {12666,12688}
X(12701) = midpoint of X(962) and X(6836)
X(12701) = reflection of X(i) in X(j) for these (i,j): (40,6922), (46,496), (56,12053), (1837,1479), (3149,946)
X(12701) = X(40)-of-2nd-Johnson-Yff-triangle
X(12701) = inner-Johnson-to-ABC similarity image of X(40)
X(12701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1836,10404), (1,9579,5434), (1,9580,6284), (1,12699,1836), (4,3057,5252), (40,9614,11), (55,946,11375), (226,12575,3303), (388,9785,5919), (497,962,65), (946,10624,55), (950,4301,2099), (1058,4295,354), (1482,9668,10572), (1697,1699,12), (2099,9670,950), (3086,6361,1155), (3579,7743,499), (3583,5697,355), (9785,9812,388)
The reciprocal orthologic center of these triangles is X(4).
X(12702) lies on these lines: {1,3}, {4,3617}, {5,962}, {8,30}, {10,381}, {20,952}, {44,1766}, {45,573}, {63,10914}, {72,3426}, {79,11237}, {100,5730}, {140,5550}, {145,376}, {149,6903}, {219,2173}, {220,5011}, {355,382}, {378,11396}, {390,12433}, {399,12778}, {474,3877}, {495,4295}, {496,1788}, {515,1657}, {519,3534}, {546,5818}, {548,1483}, {549,3616}, {550,944}, {582,595}, {631,5901}, {758,3913}, {946,1656}, {958,3647}, {960,9709}, {984,5492}, {1000,3600}, {1001,3754}, {1125,3656}, {1145,3436}, {1254,7086}, {1351,4663}, {1376,3878}, {1386,12017}, {1387,7288}, {1389,7508}, {1480,4642}, {1511,7978}, {1537,6834}, {1571,5024}, {1572,9605}, {1597,1829}, {1598,1902}, {1698,5055}, {1699,3851}, {1702,6417}, {1703,6418}, {1706,5044}, {1737,9669}, {1759,4513}, {1770,5252}, {1836,9654}, {1837,9668}, {1871,11471}, {2771,5541}, {2775,4730}, {2778,3556}, {2800,11500}, {2802,11256}, {2948,12308}, {3098,3242}, {3218,3885}, {3240,4192}, {3241,8703}, {3244,3655}, {3305,4002}, {3488,10386}, {3522,7967}, {3523,10595}, {3524,3622}, {3526,4301}, {3530,5734}, {3543,4678}, {3555,3895}, {3614,6980}, {3623,10304}, {3633,4880}, {3636,3653}, {3649,10056}, {3651,3871}, {3679,3830}, {3753,5250}, {3817,5079}, {3843,5587}, {3861,10248}, {3869,3940}, {3870,4018}, {3911,11373}, {3928,12629}, {3935,7580}, {3987,4383}, {4188,5330}, {4299,10944}, {4302,10950}, {4313,11041}, {4388,5827}, {4421,4930}, {4816,5881}, {4848,5722}, {5070,8227}, {5072,10175}, {5073,5691}, {5082,6851}, {5180,11681}, {5184,9301}, {5225,6928}, {5229,6923}, {5302,5836}, {5440,11682}, {5534,12565}, {5554,11113}, {5704,6922}, {5714,5758}, {5729,5759}, {5762,6850}, {5763,6825}, {5771,6847}, {5780,12672}, {5812,11929}, {5840,11827}, {5882,12512}, {5884,11495}, {5899,8185}, {6197,7497}, {6221,7969}, {6284,10573}, {6398,7968}, {6407,9583}, {6445,9582}, {6472,9618}, {6759,7973}, {6762,7171}, {6842,10592}, {6882,10593}, {6942,10698}, {6971,7173}, {7354,12647}, {7489,11496}, {7517,9911}, {7983,12042}, {7984,12041}, {8666,10912}, {8715,12635}, {9584,10145}, {9798,12083}, {9905,12316}, {9928,12164}, {10800,12054}, {11230,11522}, {11842,12197}, {11911,12696}, {11916,12697}, {11917,12698}, {11928,12700}
X(12702) = midpoint of X(i) and X(j) for these {i,j}: {8,6361}, {20,12245}, {40,7991}, {1657,12645}
X(12702) = reflection of X(i) in X(j) for these (i,j): (1,3579), (3,40), (4,5690), (355,11362), (381,3654), (382,355), (399,12778), (944,550), (962,5), (1482,3), (1483,548), (3241,8703), (3242,3098), (3830,3679), (4301,6684), (4930,4421), (5073,5691), (5882,12512), (6767,3587), (7973,6759), (7978,1511), (7982,1385), (7983,12042), (7984,12041), (8148,1), (8158,5709), (9301,5184), (10247,165), (10742,1145), (10912,8666), (12164,9928), (12308,2948), (12316,9905), (12635,8715), (12699,10), (12773,12515)
X(12702) = X(40)-of-X3-ABC-reflections-triangle
X(12702) = X(382)-of-1st-circumperp-triangle
X(12702) = X(1657)-of-2nd-circumperp-triangle
X(12702) = Stammler isogonal conjugate of X(3913)
X(12702) = center of circle that is the poristic locus of X(20)
X(12702) = endo-homothetic center of Ehrmann mid-triangle and outer Garcia triangle; the homothetic center is X(12699)
X(12702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,40,3579), (1,3579,3), (1,8148,1482), (3,1482,10246), (3,8148,1), (3,10247,1385), (3,10306,11849), (40,1697,3587), (40,7982,165), (46,3057,999), (57,9957,7373), (65,5119,3295), (165,7982,1385), (484,5697,56), (942,1697,6767), (942,3587,3), (1385,7982,10247), (1697,2093,942), (3057,5183,46), (3428,11248,3), (7982,10247,1482)
The reciprocal orthologic center of these triangles is X(4).
X(12703) lies on these lines: {1,3}, {4,10915}, {9,6976}, {10,6898}, {12,12700}, {119,1699}, {145,1158}, {515,3895}, {516,12115}, {528,11372}, {946,5552}, {952,1709}, {962,10528}, {1012,3880}, {1706,6983}, {1836,10956}, {1902,11400}, {2136,5881}, {2800,3870}, {2802,12775}, {3158,6326}, {3434,5587}, {3632,7330}, {3656,6174}, {3871,6261}, {3913,12672}, {5250,5554}, {5555,7160}, {5657,10596}, {5693,6765}, {5812,10955}, {5840,12749}, {6361,10805}, {7966,10860}, {9911,10834}, {10525,10827}, {10803,12197}, {10878,12497}, {10914,11496}, {10929,12697}, {10930,12698}, {10942,12699}, {10958,12701}, {11914,12696}, {12245,12514}
X(12703) = reflection of X(i) in X(j) for these (i,j): (1,10679), (40,5119)
X(12703) = X(40)-of-inner-Yff-tangents-triangle
X(12703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,165,10269), (1,2077,3576), (40,7982,12704), (65,10965,1), (962,10528,12608), (2136,12705,5881), (3057,11509,1), (5709,11010,40), (11010,11531,5709)
The reciprocal orthologic center of these triangles is X(4).
X(12704) lies on these lines: {1,3}, {4,10916}, {9,6832}, {10,6854}, {11,1728}, {30,10085}, {63,946}, {84,10431}, {191,11522}, {210,6918}, {283,4228}, {411,3873}, {496,5762}, {515,12649}, {516,12116}, {518,3149}, {580,614}, {583,8557}, {956,7686}, {962,1158}, {1068,1435}, {1072,5292}, {1125,6878}, {1329,5705}, {1473,9911}, {1699,6763}, {1708,3086}, {1709,10943}, {1766,2260}, {1768,9589}, {1836,10957}, {1902,11401}, {2270,2323}, {2360,3193}, {2802,12776}, {2829,10864}, {2949,3646}, {2990,10692}, {3306,6684}, {3436,5587}, {3475,6988}, {3555,11500}, {3681,6915}, {3811,6905}, {3868,6261}, {3870,6796}, {3916,11496}, {3928,12705}, {4005,5780}, {4333,5840}, {5231,5715}, {5437,10198}, {5603,12514}, {5657,10597}, {5720,5904}, {5722,11827}, {5735,7701}, {5805,6067}, {5881,6762}, {5905,10530}, {6326,11523}, {6361,10806}, {6907,10404}, {7580,12675}, {7682,12527}, {10526,10826}, {10804,12197}, {10879,12497}, {10884,12005}, {10931,12697}, {10932,12698}, {10949,12700}, {10959,12701}, {11915,12696}
X(12704) = reflection of X(i) in X(j) for these (i,j): (1,10680), (40,46), (11415,946)
X(12704) = X(40)-of-outer-Yff-tangents-triangle
X(12704) = X(46)-of-tangential-of-excentral-triangle
X(12704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,165,10267), (1,5536,5709), (1,5709,40), (1,11012,3576), (40,3333,3576), (40,7982,12703), (65,10966,1), (354,3338,3333), (962,3218,1158), (1699,6763,7330), (3336,7991,3359), (3359,7991,40), (4860,5584,9940), (5535,7982,40)
The reciprocal orthologic center of these triangles is X(65).
X(12705) lies on these lines: {1,84}, {3,4512}, {4,9}, {5,3359}, {11,2950}, {12,12679}, {20,5250}, {46,1699}, {55,1490}, {57,946}, {63,962}, {72,6769}, {78,12529}, {90,3577}, {104,7091}, {165,3149}, {191,9589}, {196,1712}, {200,5777}, {226,8803}, {380,5776}, {390,9799}, {495,6259}, {497,6245}, {515,1697}, {517,3927}, {595,990}, {758,6762}, {774,2263}, {936,10310}, {942,3358}, {944,4314}, {960,6282}, {968,4300}, {971,3295}, {1001,8726}, {1056,12246}, {1181,1449}, {1385,7171}, {1389,7285}, {1420,5450}, {1453,3073}, {1486,9914}, {1519,5437}, {1537,1768}, {1621,9961}, {1728,2093}, {1750,11500}, {1765,2257}, {1788,7682}, {1836,5715}, {2077,5438}, {2096,4298}, {2136,5881}, {2800,3340}, {2829,9613}, {3057,12650}, {3062,7160}, {3085,6260}, {3176,7008}, {3303,12680}, {3333,3671}, {3576,5248}, {3601,6261}, {3683,5584}, {3731,8915}, {3870,12528}, {3928,12704}, {5044,6244}, {5119,5691}, {5219,12608}, {5231,5709}, {5285,9911}, {5441,7966}, {5534,10679}, {5687,5927}, {5693,11523}, {5720,11248}, {5768,9948}, {5884,11518}, {5918,8273}, {6256,9578}, {6326,12775}, {6684,7308}, {6767,12684}, {7675,9960}, {7680,9612}, {7967,9845}, {8081,12714}, {8111,12707}, {8112,12708}, {8234,12712}, {8235,12713}, {9581,12616}, {9709,10157}, {9940,10582}, {10042,10058}, {10476,12544}, {10595,12563}
X(12705) = midpoint of X(i) and X(j) for these {i,j}: {20,9800}, {4314,9949}, {12526,12651}
X(12705) = reflection of X(i) in X(j) for these (i,j): (1,11496), (40,12514), (944,4314), (4295,946), (12520,5248), (12565,3)
X(12705) = excentral-to-hexyl similarity image of X(12565)
X(12705) = anticomplement, wrt hexyl triangle, of X(12520)
X(12705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1709,84), (1,1777,1394), (1,2956,222), (40,5587,1706), (40,11372,4), (55,12688,1490), (946,1158,57), (946,6705,3086), (1001,9943,8726), (1012,12672,1), (1519,6833,8227), (1621,9961,10884), (1768,11522,3338), (4512,12565,3), (5248,12520,3576), (5777,10306,200), (5881,12703,2136), (6212,6213,2270)
The reciprocal orthologic center of these triangles is X(65).
X(12706) lies on these lines: {7,9800}, {9,12529}, {390,6001}, {758,7673}, {1445,12565}, {3671,11025}, {7671,12560}, {7675,9960}, {7676,12514}, {7677,12520}, {7678,12609}, {7679,12617}, {8232,12688}, {8236,12709}, {8237,12712}, {8238,12713}, {8385,12707}, {8386,12708}, {8387,12714}, {8389,12716}, {8732,9943}, {9949,10865}, {10889,12548}, {11038,12710}, {11526,12651}
X(12706) = reflection of X(i) in X(j) for these (i,j): (7,12711), (12529,9)
X(12706) = excentral-to-Honsberger similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12707) lies on these lines: {363,12565}, {3671,11026}, {5934,12688}, {6001,9836}, {8107,12514}, {8109,12520}, {8111,12705}, {8113,12711}, {8133,12714}, {8377,12609}, {8380,12617}, {8385,12706}, {8390,12709}, {8391,12713}, {9783,9800}, {9943,11854}, {9949,11856}, {9961,11886}, {11039,12710}, {11527,12651}, {11685,12529}, {11892,12548}, {11922,12712}
X(12707) = excentral-to-inner-Hutson similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12708) lies on these lines: {3671,11027}, {5935,12688}, {6001,9837}, {8108,12514}, {8110,12520}, {8112,12705}, {8114,12711}, {8135,12714}, {8378,12609}, {8381,12617}, {8386,12706}, {8392,12709}, {9943,11855}, {9949,11857}, {9961,11887}, {11040,12710}, {11528,12651}, {11686,12529}, {11893,12548}, {11925,12712}, {11926,12713}
X(12708) = excentral-to-outer-Hutson similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12709) lies on these lines: {1,84}, {7,3869}, {10,12}, {11,12617}, {55,12520}, {56,392}, {57,960}, {73,3931}, {145,12529}, {227,4424}, {281,2358}, {354,12563}, {388,517}, {497,5787}, {516,3057}, {518,3340}, {942,3086}, {950,12688}, {971,3486}, {986,1465}, {997,1466}, {1042,1214}, {1062,7986}, {1319,5248}, {1400,4047}, {1420,4512}, {1617,5250}, {1697,12565}, {1788,5044}, {1837,5927}, {1858,5728}, {1864,6738}, {1898,9844}, {2099,3555}, {2646,10167}, {3304,10569}, {3339,5692}, {3476,4294}, {3600,3877}, {3601,9943}, {3666,10571}, {3812,5219}, {3868,5173}, {3873,4323}, {3878,4298}, {3884,4315}, {3890,4308}, {3893,12446}, {3899,4355}, {4313,9961}, {4314,5919}, {4551,4646}, {4870,10199}, {5018,11533}, {5083,12564}, {5252,10914}, {5439,10200}, {5440,11509}, {5693,11529}, {5694,6858}, {5784,6737}, {5836,9578}, {5884,6705}, {7681,12047}, {7686,9612}, {7962,12651}, {8236,12706}, {8239,12712}, {8240,12713}, {8390,12707}, {8392,12708}, {8543,10177}, {9785,9800}, {9949,10866}, {10480,12544}
X(12709) = midpoint of X(145) and X(12529)
X(12709) = reflection of X(i) in X(j) for these (i,j): (65,3671), (3555,12559), (4294,9957), (12526,960), (12711,1)
X(12709) = excentral-to-Hutson-intouch similarity image of X(12565)
X(12709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (12,65,3753), (65,210,4848), (1042,2292,1214), (3057,8581,10106)
The reciprocal orthologic center of these triangles is X(65).
X(12710) lies on these lines: {1,84}, {40,4326}, {65,3488}, {72,4512}, {354,1058}, {495,12617}, {496,3742}, {516,942}, {517,4314}, {518,3295}, {758,3635}, {774,2293}, {938,7671}, {943,3683}, {946,9942}, {950,5842}, {960,5248}, {962,11020}, {999,12520}, {1056,12680}, {1062,1386}, {1864,3085}, {3333,10167}, {3487,12688}, {3555,12526}, {3616,12529}, {3671,5045}, {3745,6198}, {3812,5722}, {4319,5706}, {5049,12563}, {5173,10122}, {5223,7160}, {5587,9844}, {5603,9848}, {8351,12715}, {9800,11037}, {9940,11019}, {9949,11035}, {9961,11036}, {10178,12511}, {10578,12528}, {10595,10866}, {11038,12706}, {11039,12707}, {11042,12712}, {11043,12713}, {11529,12651}
X(12710) = midpoint of X(i) and X(j) for these {i,j}: {1,12711}, {65,4294}, {3555,12526}, {4326,5728}
X(12710) = reflection of X(i) in X(j) for these (i,j): (942,12564), (960,5248), (3671,5045)
X(12710) = excentral-to-incircle-circles similarity image of X(12565)
X(12710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10391,12675), (5572,9943,942), (10122,10624,5173)
The reciprocal orthologic center of these triangles is X(65).
X(12711) lies on these lines: {1,84}, {2,12529}, {7,9800}, {8,10394}, {10,1864}, {11,5439}, {12,1898}, {33,5711}, {40,9786}, {55,72}, {56,10167}, {57,9943}, {65,516}, {174,12715}, {226,12688}, {243,1871}, {354,3671}, {380,9119}, {386,9371}, {388,971}, {390,3868}, {392,2646}, {496,10202}, {497,942}, {517,3486}, {518,1697}, {758,3057}, {774,1214}, {912,3295}, {960,3601}, {962,5173}, {1155,12511}, {1284,12713}, {1617,10884}, {1708,5584}, {1837,3753}, {2089,12714}, {2093,10399}, {2098,12559}, {2269,4047}, {2292,2293}, {3085,5777}, {3086,9940}, {3340,12651}, {3485,9856}, {3586,7686}, {3600,11220}, {3812,9581}, {3869,4313}, {3873,9785}, {3874,12575}, {3876,5281}, {3881,4342}, {3925,10395}, {5044,5218}, {5225,5806}, {5250,7675}, {5493,12432}, {5572,10384}, {5722,10525}, {5727,5836}, {5842,10572}, {7288,11227}, {8113,12707}, {8114,12708}, {8243,12712}, {8581,9949}, {10106,12680}, {10157,10588}, {10473,12544}, {10480,11997}, {10502,12570}, {10503,12568}, {10569,10866}, {10914,10950}
X(12711) = midpoint of X(i) and X(j) for these {i,j}: {7,12706}, {9800,9961}
X(12711) = reflection of X(i) in X(j) for these (i,j): (1,12710), (72,12514), (3057,4314), (3671,12564), (4295,942), (12560,5572), (12565,9943), (12672,11496), (12709,1)
X(12711) = complement of X(12529)
X(12711) = excentral-to-intouch similarity image of X(12565)
X(12711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (12,1898,5927), (55,1858,72), (354,9848,12053), (774,4300,1214), (3671,12564,354), (3753,9844,1837), (4326,12526,1697), (9856,11018,3485), (12715,12716,174)
The reciprocal orthologic center of these triangles is X(65).
X(12712) lies on these lines: {516,9808}, {3671,11030}, {6001,7596}, {8224,12514}, {8225,12520}, {8228,12609}, {8230,12617}, {8231,12565}, {8233,12688}, {8234,12705}, {8237,12706}, {8239,12709}, {8243,12711}, {8246,12713}, {9789,9800}, {9943,10858}, {9949,10867}, {9961,10885}, {10891,12548}, {11042,12710}, {11211,12566}, {11532,12651}, {11687,12529}, {11996,12716}
X(12712) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12713) lies on these lines: {21,1709}, {516,2292}, {846,12565}, {1284,12711}, {3671,11031}, {4199,12688}, {4220,12514}, {5051,12617}, {6001,9840}, {8229,12609}, {8235,12705}, {8238,12706}, {8240,12709}, {8246,12712}, {8249,12714}, {8391,12707}, {8425,12716}, {8731,9943}, {9791,9800}, {9949,10868}, {10892,12548}, {11043,12710}, {11203,12567}, {11533,12651}, {11688,12529}, {11926,12708}
X(12713) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13258)
X(12713) = excentral-to-1st-Sharygin similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
X(12714) lies on these lines: {1,12715},{516,8093}, {2089,12711}, {3671,11032}, {6001,8091}, {8075,12514}, {8077,12520}, {8078,12565}, {8079,12688}, {8081,12705}, {8084,12569}, {8085,12609}, {8087,12617}, {8133,12707}, {8135,12708}, {8241,12709}, {8247,12712}, {8249,12713}, {8387,12706}, {8733,9943}, {9793,9800}, {9961,11888}, {11192,12568}, {11690,12529}, {11894,12548}
X(12714) = reflection of X(8084) in X(12569)
X(12714) = excentral-to-tangential-midarc similarity image of X(12565)
X(12714) = reflection of X(12715) in X(1)
The reciprocal orthologic center of these triangles is X(65).
X(12715) lies on these lines: {1,12714}, {174,12711}, {258,12565}, {3671,11033}, {7588,12520}, {8083,12564}, {8125,12529}, {8351,12710}, {8734,9943}, {9949,11859}, {11895,12548}, {11899,12651}
X(12715) = excentral-to-2nd-tangential-midarc similarity image of X(12565)
X(12715) = reflection of X(12714) in X(1)
The reciprocal orthologic center of these triangles is X(65).
X(12716) lies on these lines: {174,12711}, {516,12445}, {3671,8083}, {6001,8351}, {7587,12520}, {8126,12529}, {8382,12617}, {8389,12706}, {8425,12713}, {8729,9943}, {9800,11891}, {9949,11860}, {9961,11890}, {11033,12564}, {11195,12570}, {11535,12651}, {11896,12548}, {11996,12712}
X(12716) = excentral-to-Yff-central similarity image of X(12565)
The reciprocal orthologic center of these triangles is X(65).
Let A'B'C' be the hexyl triangle. Let A" be the trilinear pole, wrt A'B'C', of line BC, and define B" and C" cyclically. Let A* be the trilinear pole, wrt A'B'C', of line B"C", and define B* and C* cyclically. The lines A'A*, B'B*, C'C* concur in X(12717). (Randy Hutson, July 21, 2017)
X(12717) lies on these lines: {1,7175}, {3,1721}, {4,9}, {20,2128}, {78,12530}, {84,309}, {515,3886}, {517,1351}, {726,6762}, {894,962}, {946,10436}, {990,3576}, {1490,12689}, {1699,2941}, {1709,1764}, {1757,7991}, {1836,10319}, {2796,3928}, {2961,5709}, {3333,3663}, {3683,9816}, {3821,5437}, {5227,5695}, {6001,10477}, {7675,12718}, {8081,12726}, {8111,12719}, {8112,12720}, {8227,12610}, {8234,12724}, {8235,12725}, {8726,9944}, {9950,10864}, {9962,10884}
X(12717) = midpoint of X(i) and X(j) for these {i,j}: {1,7996}, {20,9801}
X(12717) = reflection of X(i) in X(j) for these (i,j): (40,1766), (1721,3)
X(12717) = X(317)-of-hexyl-triangle
X(12717) = excentral-to-hexyl similarity image of X(1721)
X(12717) = hexyl-isotomic conjugate of X(84)
X(12717) = anticomplement, wrt hexyl triangle, of X(990)
X(12717) = {X(40), X(11372)}-harmonic conjugate of X(6210)
The reciprocal orthologic center of these triangles is X(65).
X(12718) lies on these lines: {7,9801}, {9,12530}, {990,7677}, {1445,1721}, {1766,7676}, {3663,11025}, {4326,7996}, {7675,12717}, {7678,12610}, {7679,12618}, {8232,12689}, {8236,12721}, {8237,12724}, {8238,12725}, {8385,12719}, {8386,12720}, {8387,12726}, {8389,12728}, {8732,9944}, {9950,10865}, {10889,12549}, {11038,12722}, {11526,12652}
X(12718) = reflection of X(i) in X(j) for these (i,j): (7,12723), (12530,9)
X(12718) = X(317)-of-Honsberger-triangle
X(12718) = excentral-to-Honsberger similarity image of X(1721)
X(12718) = Honsberger-isotomic conjugate of X(12669)
The reciprocal orthologic center of these triangles is X(65).
X(12719) lies on these lines: {363,1721}, {990,8109}, {1766,8107}, {3663,11026}, {5934,12689}, {7996,8140}, {8111,12717}, {8113,12723}, {8133,12726}, {8377,12610}, {8380,12618}, {8385,12718}, {8390,12721}, {8391,12725}, {9783,9801}, {9944,11854}, {9950,11856}, {9962,11886}, {11039,12722}, {11527,12652}, {11685,12530}, {11892,12549}, {11922,12724}
X(12719) = reflection of X(12720) in X(7996)
X(12719) = X(317)-of-inner-Hutson-triangle
X(12719) = excentral-to-inner-Hutson similarity image of X(1721)
X(12719) = inner-Hutson-isotomic conjugate of X(12673)
The reciprocal orthologic center of these triangles is X(65).
X(12720) lies on these lines: {990,8110}, {1766,8108}, {3663,11027}, {5935,12689}, {7996,8140}, {8112,12717}, {8114,12723}, {8135,12726}, {8378,12610}, {8381,12618}, {8386,12718}, {8392,12721}, {9944,11855}, {9950,11857}, {9962,11887}, {11040,12722}, {11528,12652}, {11686,12530}, {11893,12549}, {11925,12724}, {11926,12725}
X(12720) = reflection of X(12719) in X(7996)
X(12720) = X(317)-of-outer-Hutson-triangle
X(12720) = excentral-to-outer-Hutson similarity image of X(1721)
X(12720) = outer-Hutson-isotomic conjugate of X(12674)
The reciprocal orthologic center of these triangles is X(65).
X(12721) lies on these lines: {1,7175}, {11,12618}, {12,12610}, {38,1824}, {55,990}, {56,1766}, {65,3663}, {72,726}, {145,12530}, {210,3030}, {354,4353}, {392,3923}, {516,3057}, {517,1469}, {518,3875}, {537,4523}, {950,12689}, {960,3729}, {971,3056}, {1362,2823}, {1682,10445}, {1697,1721}, {3601,9944}, {3688,5784}, {3753,3821}, {4313,9962}, {4660,10914}, {7962,12652}, {8236,12718}, {8239,12724}, {8240,12725}, {8241,12726}, {8390,12719}, {8392,12720}, {9785,9801}, {9950,10866}, {10444,10480}, {10544,12680}, {11924,12728}
X(12721) = midpoint of X(145) and X(12530)
X(12721) = reflection of X(i) in X(j) for these (i,j): (65,3663), (3729,960), (10914,4660), (12723,1)
X(12721) = X(317)-of-Hutson-intouch-triangle
X(12721) = excentral-to-Hutson-intouch similarity image of X(1721)
X(12721) = Hutson-intouch-isotomic conjugate of X(12672)
The reciprocal orthologic center of these triangles is X(65).
X(12722) lies on these lines: {1,7175}, {495,12618}, {496,12610}, {516,942}, {518,3923}, {990,999}, {1721,3333}, {1766,3295}, {3487,12689}, {3555,3729}, {3663,5045}, {3742,3821}, {3812,4660}, {4353,5049}, {5255,6211}, {8351,12727}, {9801,11037}, {9950,11035}, {9962,11036}, {11038,12718}, {11039,12719}, {11040,12720}, {11042,12724}, {11043,12725}, {11529,12652}
X(12722) = midpoint of X(i) and X(j) for these {i,j}: {1,12723}, {3555,3729}
X(12722) = reflection of X(i) in X(j) for these (i,j): (3663,5045), (4660,3812)
X(12722) = X(317)-of-incircle-circles-triangle
X(12722) = excentral-to-incircle-circles similarity image of X(1721)
X(12722) = incircle-circles-isotomic conjugate of X(12675)
X(12722) = anticomplement, wrt incircle-circles triangle, of X(4353)
The reciprocal orthologic center of these triangles is X(65).
X(12723) lies on these lines: {1,7175}, {2,12530}, {4,4008}, {7,9801}, {11,12610}, {12,12618}, {19,6059}, {31,1824}, {33,1460}, {37,2223}, {55,1766}, {56,990}, {57,1721}, {65,516}, {72,3923}, {174,12727}, {181,1864}, {226,12689}, {354,3663}, {517,3056}, {518,3729}, {604,4336}, {726,3555}, {971,1469}, {1108,4516}, {1122,4014}, {1284,12725}, {1359,2823}, {1400,1827}, {1418,3675}, {1742,7146}, {1871,3073}, {1872,3072}, {1876,4331}, {1900,5230}, {2089,12726}, {2171,2293}, {2175,2182}, {2262,3271}, {2285,4319}, {2309,3010}, {2356,8898}, {2805,4852}, {3340,12652}, {3501,4073}, {3753,4660}, {3821,5439}, {3941,8609}, {4523,4672}, {8113,12719}, {8114,12720}, {8243,12724}, {8581,9950}, {10391,10444}
X(12723) = midpoint of X(i) and X(j) for these {i,j}: {7,12718}, {9801,9962}
X(12723) = reflection of X(i) in X(j) for these (i,j): (1,12722), (72,3923), (1721,9944), (4523,4672), (12721,1)
X(12723) = complement of X(12530)
X(12723) = {X(12727), X(12728)}-harmonic conjugate of X(174)
X(12723) = X(317)-of-intouch-triangle
X(12723) = excentral-to-intouch similarity image of X(1721)
X(12723) = intouch-isogonal conjugate of X(222)
X(12723) = intouch-isotomic conjugate of X(1071)
X(12723) = anticomplement, wrt intouch triangle, of X(3663)
The reciprocal orthologic center of these triangles is X(65).
X(12724) lies on these lines: {516,9808}, {990,8225}, {1721,8231}, {1766,8224}, {3663,11030}, {3817,8228}, {7996,8244}, {8230,12618}, {8233,12689}, {8234,12717}, {8237,12718}, {8239,12721}, {8243,12723}, {8246,12725}, {8247,12726}, {9789,9801}, {9944,10858}, {9950,10867}, {9962,10885}, {10891,12549}, {11042,12722}, {11532,12652}, {11687,12530}, {11922,12719}, {11925,12720}, {11996,12728}
X(12724) = X(317)-of-2nd-Pamfilos-Zhou-triangle
X(12724) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(1721)
X(12724) = 2nd-Pamfilos-Zhou-isotomic conjugate of X(12681)
The reciprocal orthologic center of these triangles is X(65).
X(12725) lies on these lines: {4,240}, {21,990}, {165,846}, {516,2292}, {1284,12723}, {3663,11031}, {4199,12689}, {5051,8582}, {8229,12610}, {8235,12717}, {8238,12718}, {8240,12721}, {8246,12724}, {8249,12726}, {8391,12719}, {8425,12728}, {8731,9944}, {9791,9801}, {10892,12549}, {11043,12722}, {11533,12652}, {11688,12530}, {11926,12720}
X(12725) = X(317)-of-1st-Sharygin-triangle
X(12725) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13259)
X(12725) = excentral-to-1st-Sharygin similarity image of X(1721)
X(12725) = hexyl-to-1st-Sharygin similarity image of X(12717)
X(12725) = 1st-Sharygin-isotomic conjugate of X(12682)
The reciprocal orthologic center of these triangles is X(65).
X(12726) lies on these lines: {1,12727}, {516,8093}, {990,8077}, {1721,8078}, {1766,8075}, {2089,12723}, {3663,11032}, {7996,8089}, {8079,12689}, {8081,12717}, {8085,12610}, {8087,12618}, {8133,12719}, {8135,12720}, {8241,12721}, {8247,12724}, {8249,12725}, {8387,12718}, {8733,9944}, {9793,9801}, {9962,11888}, {11690,12530}, {11894,12549}
X(12726) = reflection of X(12727) in X(1)
X(12726) = X(317)-of-tangential-midarc-triangle
X(12726) = excentral-to-tangential-midarc similarity image of X(1721)
X(12726) = tangential-midarc-isotomic conjugate of X(8095)
The reciprocal orthologic center of these triangles is X(65).
X(12727) lies on these lines: {1,12726}, {174,12723}, {258,1721}, {990,7588}, {3663,11033}, {8125,12530}, {8351,12722}, {8734,9944}, {9950,11859}, {11895,12549}, {11899,12652}
X(12727) = reflection of X(12726) in X(1)
X(12727) = X(317)-of-2nd-tangential-midarc-triangle
X(12727) = excentral-to-2nd-tangential-midarc similarity image of X(1721)
X(12727) = 2nd-tangential-midarc-isotomic conjugate of X(8096)
X(12727) = {X(174), X(12723)}-harmonic conjugate of X(12728)
The reciprocal orthologic center of these triangles is X(65).
X(12728) lies on these lines: {174,12723}, {516,12445}, {990,7587}, {3663,8083}, {8126,12530}, {8382,12618}, {8389,12718}, {8425,12725}, {8729,9944}, {9801,11891}, {9950,11860}, {9962,11890}, {11535,12652}, {11924,12721}, {11996,12724}
X(12728) = {X(174), X(12723)}-harmonic conjugate of X(12727)
X(12728) = X(317)-of-Yff-central-triangle
X(12728) = excentral-to-Yff-central similarity image of X(1721)
X(12728) = Yff-central-isotomic conjugate of X(12685)
The reciprocal orthologic center of these triangles is X(3).
X(12729) lies on these lines: {11,11831}, {30,6265}, {80,402}, {100,11900}, {214,1650}, {515,12752}, {952,12438}, {2771,12790}, {2800,12113}, {2802,12626}, {2829,12668}, {4240,6224}, {5840,12696}, {6262,11902}, {6263,11901}, {7972,11910}, {9897,11852}, {9912,11853}, {10057,11912}, {10073,11913}, {11832,12137}, {11839,12198}, {11845,12247}, {11848,12331}, {11863,12460}, {11864,12461}, {11885,12498}, {11903,12737}, {11904,12738}, {11905,12739}, {11906,12740}, {11907,12741}, {11908,12742}, {11909,12743}, {11911,12747}, {11914,12749}, {11915,12750}
X(12729) = midpoint of X(4240) and X(6224)
X(12729) = reflection of X(i) in X(j) for these (i,j): (80,402), (1650,214)
X(12729) = X(80)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(8).
X(12730) lies on these lines: {7,528}, {9,12531}, {11,7679}, {80,2346}, {100,2078}, {119,7678}, {145,5856}, {390,952}, {516,7972}, {517,12755}, {1387,6854}, {1445,5541}, {2800,7673}, {2802,7672}, {4326,7993}, {5219,10707}, {5252,8543}, {5854,12630}, {6264,7675}, {8097,8387}, {8098,8388}, {8232,12690}, {8237,12744}, {8238,12746}, {8385,12733}, {8386,12734}, {8389,12748}, {8732,9945}, {9951,10865}, {10889,12550}, {11025,12736}, {11038,12735}, {11526,12653}
X(12730) = reflection of X(i) in X(j) for these (i,j): (7,1317), (1156,390), (12531,9)
X(12730) = X(74)-of-Honsberger-triangle
X(12730) = excentral-to-Honsberger similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(12732).
X(12731) lies on these lines: {1,12521}, {1158,5493}, {2475,9874}, {3625,6849}, {5082,9953}, {7160,12620}, {9782,9804}
X(12731) = reflection of X(7160) in X(12620)
X(12731) lies on the Jerabek hyperbola of the Fuhrmann triangle.
The reciprocal orthologic center of these triangles is X(12731).
X(12732) lies on these lines: {9,80}, {11,3634}, {20,952}, {65,1317}, {100,474}, {149,5084}, {214,3748}, {392,9951}, {1320,9945}, {1537,12331}, {1617,2932}, {2094,6224}, {3871,5719}, {3895,11112}, {4304,10914}, {6957,10738}
X(12732) = reflection of X(i) in X(j) for these (i,j): (1145,5541), (1320,9945), (1537,12331), (9802,1387), (10609,6154), (12690,1145)
X(12732) = {X(100), X(9802)}-harmonic conjugate of X(1387)
The reciprocal orthologic center of these triangles is X(8).
X(12733) lies on these lines: {11,8380}, {100,8109}, {104,8107}, {119,8377}, {363,5541}, {517,12759}, {952,9836}, {1317,8113}, {5854,12633}, {5934,12690}, {6264,8111}, {7993,8140}, {8097,8133}, {8385,12730}, {8391,12746}, {9783,9802}, {9945,11854}, {9951,11856}, {9963,11886}, {11026,12736}, {11039,12735}, {11527,12653}, {11685,12531}, {11892,12550}, {11922,12744}
X(12733) = reflection of X(12734) in X(7993)
X(12733) = X(74)-of-inner-Hutson-triangle
X(12733) = excentral-to-inner-Hutson similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(8).
X(12734) lies on these lines: {11,8381}, {100,8110}, {104,8108}, {119,8378}, {517,12760}, {952,9837}, {1317,8114}, {5854,12634}, {5935,12690}, {6264,8112}, {7993,8140}, {8097,8135}, {8098,8138}, {8386,12730}, {9945,11855}, {9951,11857}, {9963,11887}, {11027,12736}, {11040,12735}, {11528,12653}, {11686,12531}, {11893,12550}, {11925,12744}, {11926,12746}
X(12734) = reflection of X(12733) in X(7993)
X(12734) = X(74)-of-outer-Hutson-triangle
X(12734) = excentral-to-outer-Hutson similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(8).
X(12735) lies on these lines: {1,5}, {30,5048}, {55,10074}, {56,10087}, {100,999}, {104,3295}, {145,1145}, {149,1056}, {153,1058}, {214,3244}, {388,10738}, {390,6938}, {497,10742}, {517,5083}, {519,3035}, {528,5542}, {551,6667}, {631,7317}, {942,2802}, {944,1537}, {1125,3036}, {1319,5844}, {1320,3296}, {1388,5690}, {1479,12763}, {1482,4293}, {1862,1870}, {2098,4302}, {2099,11046}, {2800,9957}, {2829,4342}, {3057,11570}, {3303,10058}, {3304,10090}, {3333,5541}, {3340,10993}, {3476,10247}, {3487,12690}, {3576,8275}, {3616,12531}, {3636,6702}, {3655,7962}, {3890,12532}, {4311,11278}, {4312,12119}, {5045,12736}, {5049,6797}, {5218,10246}, {5556,5734}, {5919,12758}, {6154,11034}, {6198,12138}, {6767,12773}, {7373,12331}, {9802,11037}, {9951,11035}, {9963,11036}, {11011,11551}, {11038,12730}, {11039,12733}, {11040,12734}, {11042,12744}, {11043,12746}, {12053,12611}
X(12735) = midpoint of X(i) and X(j) for these {i,j}: {1,1317}, {11,7972}, {145,1145}, {214,3244}, {944,1537}, {1320,10609}, {3057,11570}, {6154,12653}
X(12735) = reflection of X(i) in X(j) for these (i,j): (1387,1), (3036,1125), (6702,3636), (12019,1387), (12736,5045)
X(12735) = incircle-inverse-of-X(7972)
X(12735) = X(74)-of-incircle-circles-triangle
X(12735) = excentral-to-incircle-circles similarity image of X(5541)
X(12735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,5252,10283), (1,7972,11), (1,10944,5901), (11,1317,7972), (944,4345,9668)
The reciprocal orthologic center of these triangles is X(8).
X(12736) lies on these lines: {1,88}, {7,80}, {8,11023}, {11,65}, {46,10058}, {56,11715}, {57,104}, {119,226}, {142,1145}, {149,938}, {354,1317}, {388,12751}, {499,3878}, {517,1387}, {518,3036}, {519,5570}, {528,5572}, {653,1845}, {758,908}, {942,952}, {950,5840}, {954,6594}, {960,6667}, {999,12737}, {1155,5427}, {1156,10398}, {1411,11700}, {1445,2093}, {1768,3339}, {1771,3924}, {1836,12764}, {1837,5884}, {1876,12138}, {1938,10006}, {2099,12740}, {2771,7687}, {2829,4292}, {2840,3937}, {3035,3812}, {3057,10165}, {3333,6264}, {3338,10074}, {3340,10698}, {3486,12119}, {3586,10724}, {3738,10015}, {3873,12531}, {3874,10057}, {3887,11028}, {3918,10039}, {3919,9951}, {4345,5697}, {4654,10711}, {5045,12735}, {5328,5692}, {5587,12665}, {5708,12773}, {5722,10738}, {5728,12690}, {5836,5854}, {6147,11698}, {6326,11529}, {6738,10122}, {7993,10980}, {8083,12748}, {8097,11032}, {9579,10728}, {9802,10580}, {9945,11018}, {9963,11020}, {10404,12763}, {10532,12247}, {10950,12005}, {11021,12550}, {11025,12730}, {11026,12733}, {11027,12734}, {11030,12744}, {11031,12746}
X(12736) = midpoint of X(i) and X(j) for these {i,j}: {11,65}, {80,11570}, {942,6797}
X(12736) = reflection of X(i) in X(j) for these (i,j): (960,6667), (3035,3812), (5083,942), (12735,5045)
X(12736) = incircle-inverse-of-X(106)
X(12736) = X(74)-of-inverse-in-incircle-triangle
X(12736) = X(113)-of-intouch-triangle
X(12736) = complement, wrt intouch triangle, of X(1317)
X(12736) = excentral-to-inverse-in-incircle similarity image of X(5541)
X(12736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10090,214), (80,5902,11570), (1320,3306,214), (1737,8068,6702)
The reciprocal orthologic center of these triangles is X(3).
X(12737) lies on these lines: {1,5}, {3,2802}, {8,12619}, {40,12653}, {65,10074}, {100,1385}, {104,517}, {145,6972}, {149,944}, {153,5603}, {214,1376}, {515,10738}, {519,10265}, {528,3655}, {912,5048}, {946,10742}, {962,12248}, {997,3036}, {999,12736}, {1319,10090}, {1389,6583}, {1482,2800}, {1537,3656}, {1538,10707}, {1768,7982}, {2098,12758}, {2099,11570}, {2646,10087}, {2771,7984}, {2801,10247}, {2827,6095}, {2829,12676}, {2932,10269}, {3057,10058}, {3241,9803}, {3244,12616}, {3434,6224}, {3576,5541}, {3653,6174}, {3898,7489}, {4511,12531}, {5330,5694}, {5731,9802}, {5734,9809}, {5790,6702}, {5840,12700}, {5844,11219}, {6175,10031}, {6262,10920}, {6263,10919}, {6906,10284}, {9912,10829}, {10522,10806}, {10679,12332}, {10794,12198}, {10871,12498}, {10945,12741}, {10946,12742}, {10947,12743}, {11009,11571}, {11014,11826}, {11224,12767}, {11390,12137}, {11865,12460}, {11866,12461}, {11903,12729}, {11928,12747}, {12047,12763}
X(12737) = midpoint of X(i) and X(j) for these {i,j}: {1,6264}, {40,12653}, {104,1320}, {145,12247}, {149,944}, {962,12248}, {1482,12773}, {1768,7982}, {6326,7993}
X(12737) = reflection of X(i) in X(j) for these (i,j): (3,11715), (8,12619), (80,1484), (100,1385), (119,1387), (153,12611), (355,11), (1145,6713), (5660,10283), (6265,1), (7972,1483), (10742,946), (11698,5901), (12331,214), (12515,104), (12738,6265), (12751,5)
X(12737) = hexyl circle-inverse-of-X(7993)
X(12737) = X(80)-of-inner-Johnson-triangle
X(12737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,80,12740), (1,7972,12739), (1,7993,6326), (11,10944,10057), (119,1387,5886), (153,5603,12611), (7972,10057,10944), (10246,12331,214)
The reciprocal orthologic center of these triangles is X(3).
X(12738) lies on these lines: {1,5}, {3,2801}, {35,3652}, {72,74}, {78,10609}, {104,6986}, {140,11219}, {149,12611}, {153,6895}, {200,3654}, {214,958}, {500,5293}, {515,12762}, {517,3935}, {528,3811}, {912,1155}, {943,1156}, {997,3655}, {1259,2932}, {1385,5260}, {1490,5528}, {2800,11500}, {2802,8148}, {2829,12677}, {3035,5791}, {3436,6224}, {3617,10786}, {3634,10265}, {3656,3870}, {4860,6911}, {5204,12757}, {5217,12665}, {5221,11570}, {5694,11491}, {5708,9946}, {5812,5840}, {6262,10922}, {6263,10921}, {6583,6915}, {8167,10246}, {9780,9803}, {9912,10830}, {9955,10707}, {9963,10728}, {10698,11278}, {10742,12437}, {10795,12198}, {10872,12498}, {10951,12741}, {10952,12742}, {10953,12743}, {11391,12137}, {11827,12119}, {11867,12460}, {11868,12461}, {11904,12729}, {11929,12747}
X(12738) = midpoint of X(i) and X(j) for these {i,j}: {5531,6326}, {9963,10728}
X(12738) = reflection of X(i) in X(j) for these (i,j): (80,11698), (149,12611), (6265,6326), (9803,12619), (12515,100), (12737,6265), (12773,214)
X(12738) = X(80)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12739) lies on these lines: {1,5}, {3,10093}, {4,12743}, {21,12532}, {35,11571}, {55,2800}, {56,214}, {59,518}, {65,100}, {78,3035}, {104,943}, {149,3485}, {153,3486}, {388,6224}, {498,12619}, {515,12763}, {517,10087}, {758,5172}, {942,10090}, {950,12764}, {954,2801}, {956,1388}, {1145,3811}, {1320,11011}, {1385,10074}, {1454,12559}, {1464,5018}, {1479,12611}, {1537,6261}, {1768,3601}, {1836,5840}, {2078,4867}, {2099,2802}, {2771,10058}, {2829,12678}, {2932,11509}, {3057,10698}, {3085,12247}, {3295,12758}, {3340,5541}, {3868,4996}, {3870,5854}, {4305,12248}, {4313,9809}, {4321,5856}, {4323,9802}, {4861,11256}, {4870,10707}, {5528,12560}, {5538,5762}, {5703,9803}, {5730,11510}, {5851,7675}, {6001,12775}, {6262,10924}, {6263,10923}, {7354,12119}, {9654,12747}, {9912,10831}, {10404,10609}, {10572,10742}, {10738,12047}, {10797,12198}, {10873,12498}, {11392,12137}, {11501,12331}, {11870,12461}, {11905,12729}, {11930,12741}, {11931,12742}
X(12739) = midpoint of X(i) and X(j) for these {i,j}: {1317,10956}, {7972,10057}
X(12739) = reflection of X(i) in X(j) for these (i,j): (5252,10956), (10057,495)
X(12739) = X(80)-of-1st-Johnson-Yff-triangle
X(12739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,4551,1411), (1,6265,12740), (1,6326,11), (1,7972,12737), (35,11571,12515), (214,5083,56), (495,10944,5252), (1317,10944,7972)
The reciprocal orthologic center of these triangles is X(3).
X(12740) lies on these lines: {1,5}, {3,10094}, {33,5151}, {36,12515}, {55,214}, {56,2800}, {65,10698}, {78,5854}, {100,3057}, {104,1319}, {106,10703}, {153,3476}, {497,6224}, {499,12619}, {515,12764}, {517,10090}, {997,1145}, {999,11570}, {1318,1320}, {1385,10058}, {1388,11715}, {1420,1768}, {1470,12332}, {1478,12611}, {1519,12761}, {1537,1836}, {1964,4336}, {2098,2802}, {2099,12736}, {2646,10179}, {2771,10074}, {2829,12679}, {3086,12247}, {3254,6596}, {3304,5083}, {3877,4996}, {4308,9809}, {4345,9802}, {5433,11014}, {5541,7962}, {5563,11571}, {5840,12701}, {6262,10926}, {6263,10925}, {6284,12119}, {6958,10043}, {9669,12747}, {9912,10832}, {9957,10087}, {10106,12763}, {10798,12198}, {10874,12498}, {11256,12531}, {11393,12137}, {11502,12331}, {11871,12460}, {11872,12461}, {11906,12729}, {11932,12741}, {11933,12742}
X(12740) = reflection of X(i) in X(j) for these (i,j): (1837,11), (2932,214), (10073,496)
X(12740) = X(80)-of-2nd-Johnson-Yff-triangle
X(12740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,80,12737), (1,6265,12739), (1,6326,1317), (497,6224,12743)
The reciprocal orthologic center of these triangles is X(3).
X(12741) lies on these lines: {11,11377}, {80,493}, {100,8214}, {214,8222}, {515,12765}, {952,12440}, {2800,9838}, {2802,12636}, {6224,6462}, {6262,8218}, {6263,8216}, {6265,8220}, {6461,12742}, {7972,8210}, {8188,9897}, {8194,9912}, {10057,11951}, {10073,11953}, {10875,12498}, {10945,12737}, {10951,12738}, {11394,12137}, {11503,12331}, {11828,12119}, {11840,12198}, {11846,12247}, {11907,12729}, {11930,12739}, {11932,12740}, {11947,12743}, {11949,12747}, {11955,12749}, {11957,12750}
X(12741) = X(80)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12742) lies on these lines: {11,11378}, {80,494}, {100,8215}, {214,8223}, {515,12766}, {952,12441}, {2800,9839}, {2802,12637}, {6224,6463}, {6262,8219}, {6263,8217}, {6265,8221}, {6461,12741}, {7972,8211}, {8189,9897}, {8195,9912}, {10057,11952}, {10073,11954}, {10876,12498}, {10946,12737}, {10952,12738}, {11395,12137}, {11504,12331}, {11829,12119}, {11841,12198}, {11847,12247}, {11908,12729}, {11931,12739}, {11933,12740}, {11948,12743}, {11950,12747}, {11956,12749}, {11958,12750}
X(12742) = X(80)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12743) lies on these lines: {1,10738}, {3,10073}, {4,12739}, {11,214}, {30,11570}, {33,12137}, {35,12619}, {55,80}, {56,12119}, {65,5840}, {100,1837}, {149,3486}, {355,10087}, {497,6224}, {515,1317}, {952,1898}, {1385,5533}, {1479,6265}, {1697,9897}, {1836,10724}, {2098,7972}, {2800,6284}, {2802,10950}, {2829,12680}, {2932,11502}, {3295,10057}, {3583,12611}, {3586,6326}, {4294,12247}, {4302,12515}, {4304,10265}, {4542,5853}, {5083,7354}, {5432,6702}, {5541,5727}, {5691,12763}, {5722,10090}, {6262,10928}, {6263,10927}, {9912,10833}, {10698,12701}, {10799,12198}, {10877,12498}, {10947,12737}, {10953,12738}, {10965,12749}, {10966,12750}, {11114,12532}, {11873,12460}, {11909,12729}, {11947,12741}, {11948,12742}
X(12743) = reflection of X(i) in X(j) for these (i,j): (11,950), (7354,5083)
X(12743) = X(80)-of-Mandart-incircle-triangle
X(12743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497,6224,12740), (3295,12747,10057), (3586,6326,12764)
The reciprocal orthologic center of these triangles is X(8).
X(12744) lies on these lines: {11,8230}, {80,7133}, {100,8225}, {104,8224}, {119,8228}, {517,12768}, {952,7596}, {1317,8243}, {1320,7595}, {2800,12681}, {2802,9808}, {5541,8231}, {5854,12638}, {6264,8234}, {7993,8244}, {8097,8247}, {8098,8248}, {8233,12690}, {8237,12730}, {8246,12746}, {9789,9802}, {9945,10858}, {9951,10867}, {9963,10885}, {10891,12550}, {11030,12736}, {11042,12735}, {11532,12653}, {11687,12531}, {11922,12733}, {11925,12734}, {11996,12748}
X(12744) = X(74)-of-2nd-Pamfilos-Zhou-triangle
X(12744) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(11604).
X(12745) lies on the Jerabek hyperbola of trhe Furhmann triangle and these lines: {1,6597}, {8,6595}, {191,12342}, {1158,12519}, {2476,9782}, {10266,12623}
X(12745) = midpoint of X(6597) and X(12786)
X(12745) = reflection of X(i) in X(j) for these (i,j): (10266,12623), (12342,191)
The reciprocal orthologic center of these triangles is X(8).
X(12746) lies on these lines: {1,3909}, {10,21}, {11,5051}, {104,4220}, {119,8229}, {256,1320}, {517,12770}, {846,5541}, {855,1145}, {952,9840}, {1281,2787}, {1284,1317}, {2292,2802}, {2800,12683}, {4199,12690}, {5854,12642}, {6264,8235}, {7993,8245}, {8097,8249}, {8098,8250}, {8238,12730}, {8246,12744}, {8391,12733}, {8425,12748}, {8731,9945}, {9791,9802}, {9951,10868}, {10892,12550}, {11031,12736}, {11043,12735}, {11533,12653}, {11688,12531}, {11926,12734}
X(12746) = X(74)-of-1st-Sharygin-triangle
X(12746) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13266)
X(12746) = excentral-to-1st-Sharygin similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(3).
X(12747) lies on these lines: {3,80}, {4,145}, {5,6224}, {11,6980}, {30,12247}, {40,3065}, {100,5790}, {214,1656}, {355,8715}, {382,2800}, {515,12773}, {517,9897}, {528,5779}, {944,1484}, {999,10073}, {1598,12137}, {1657,12515}, {2771,5691}, {2802,12645}, {2829,12684}, {3036,10993}, {3295,10057}, {3526,6702}, {3843,12611}, {5180,5844}, {5727,6797}, {5840,11827}, {6262,11917}, {6263,11916}, {6862,10609}, {6863,12019}, {6892,9945}, {7517,9912}, {7972,10247}, {9301,12498}, {9654,12739}, {9655,11570}, {9668,12758}, {9669,12740}, {10679,12751}, {11842,12198}, {11875,12460}, {11876,12461}, {11911,12729}, {11928,12737}, {11929,12738}, {11949,12741}, {11950,12742}, {12000,12749}, {12001,12750}
X(12747) = reflection of X(i) in X(j) for these (i,j): (3,80), (944,1484), (1482,10738), (1657,12515), (6224,5), (10993,3036), (12119,12619), (12331,355)
X(12747) = X(80)-of-X3-ABC-reflections-triangle
X(12747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (80,12119,12619), (10057,12743,3295)
The reciprocal orthologic center of these triangles is X(8).
X(12748) lies on these lines: {11,8382}, {100,7587}, {174,1317}, {517,12774}, {952,8351}, {2800,12685}, {2802,12445}, {5854,12646}, {7993,8423}, {8083,12736}, {8126,12531}, {8389,12730}, {8425,12746}, {8729,9945}, {9802,11891}, {9951,11860}, {9963,11890}, {11535,12653}, {11896,12550}, {11996,12744}
X(12748) = X(74)-of-Yff-central-triangle
X(12748) = excentral-to-Yff-central similarity image of X(5541)
The reciprocal orthologic center of these triangles is X(3).
X(12749) lies on these lines: {1,5}, {8,10940}, {10,10074}, {36,6735}, {46,1145}, {79,12641}, {100,10915}, {104,10039}, {153,10935}, {214,5552}, {498,11715}, {515,10087}, {517,12763}, {956,5445}, {1320,12047}, {1478,2802}, {1768,11919}, {2098,12611}, {2800,12115}, {2829,5119}, {3057,10742}, {5083,10573}, {5541,9613}, {5697,6256}, {5840,12703}, {5856,9814}, {6224,10528}, {6262,10930}, {6263,10929}, {9612,12653}, {9912,10834}, {9957,12764}, {10090,10106}, {10698,12608}, {10803,12198}, {10805,12247}, {10878,12498}, {10965,12743}, {10970,12767}, {11248,12119}, {11400,12137}, {11509,12331}, {11881,12460}, {11882,12461}, {11914,12729}, {11955,12741}, {11956,12742}, {12000,12747}
X(12749) = reflection of X(i) in X(j) for these (i,j): (1,10956), (80,10057), (10057,5252)
X(12749) = X(80)-of-inner-Yff-tangents-triangle
X(12749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,12751,80), (80,7972,12750), (355,10073,80), (1317,11729,1), (10942,10944,1)
The reciprocal orthologic center of these triangles is X(3).
X(12750) lies on these lines: {1,5}, {35,11219}, {46,528}, {79,3254}, {100,10916}, {149,4295}, {214,10527}, {515,12776}, {1478,3892}, {1479,2801}, {1768,11920}, {1898,4857}, {2771,12374}, {2800,12116}, {2802,12649}, {2829,12687}, {4311,10074}, {4314,10058}, {4333,5840}, {5083,11048}, {5086,10031}, {5445,5687}, {6224,10529}, {6262,10932}, {6263,10931}, {9785,9803}, {9912,10835}, {10087,10265}, {10707,12047}, {10804,12198}, {10806,12247}, {10879,12498}, {10966,12743}, {10971,12767}, {11249,12119}, {11401,12137}, {11510,12331}, {11883,12460}, {11884,12461}, {11915,12729}, {11957,12741}, {11958,12742}, {12001,12747}
X(12750) = reflection of X(80) in X(10073)
X(12750) = X(80)-of-outer-Yff-tangents-triangle
X(12750) = {X(80), X(7972)}-harmonic conjugate of X(12749)
The reciprocal orthologic center of these triangles is X(40).
X(12751) lies on the cubic K684 and these lines: {1,5}, {2,11715}, {4,2802}, {8,153}, {10,104}, {40,1145}, {65,12763}, {72,12762}, {100,515}, {214,944}, {388,12736}, {516,10728}, {517,10742}, {519,1519}, {528,11372}, {529,5535}, {912,11571}, {946,1320}, {1482,12611}, {1537,5854}, {1698,6713}, {1699,12653}, {1737,5193}, {1768,3359}, {2550,2801}, {2787,9864}, {2806,12784}, {2827,4768}, {2932,12114}, {3035,3576}, {3036,5794}, {3057,12764}, {3419,11525}, {3813,11256}, {3898,6965}, {4413,5790}, {4668,12767}, {4996,6796}, {5086,12531}, {5090,12138}, {5541,5691}, {5552,6224}, {5554,9803}, {5657,12248}, {5687,12332}, {5688,12754}, {5689,12753}, {5690,12515}, {5787,9945}, {5818,6702}, {5847,10759}, {6797,8581}, {8193,9913}, {8197,12462}, {8204,12463}, {8214,12765}, {8215,12766}, {9857,12499}, {10039,10058}, {10087,10572}, {10573,11570}, {10679,12747}, {10707,10863}, {10791,12199}, {10914,12761}, {10915,12775}, {10916,12776}, {11248,12331}, {11362,11684}, {11900,12752}, {12647,12758}
X(12751) = midpoint of X(i) and X(j) for these {i,j}: {8,153}, {5531,9897}, {5541,5691}, {5881,6326}
X(12751) = reflection of X(i) in X(j) for these (i,j): (1,119), (40,1145), (80,355), (104,10), (944,214), (1320,946), (1482,12611), (2077,6735), (5693,12665), (6264,11), (6265,11698), (7972,6265), (7982,1537), (11219,5790), (11256,3813), (12119,100), (12515,5690), (12737,5), (12773,12619)
X(12751) = anticomplement of X(11715)
X(12751) = Fuhrmann circle-inverse-of-X(5881)
X(12751) = X(104)-of-outer-Garcia-triangle
X(12751) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (80,7972,10073), (80,12749,1), (355,5252,5587), (5587,6264,11), (5660,7972,6265), (5790,12773,12619)
The reciprocal orthologic center of these triangles is X(40).
X(12752) lies on these lines: {11,11897}, {30,100}, {104,402}, {119,1650}, {153,4240}, {515,12729}, {952,11251}, {1317,11909}, {1768,11852}, {2787,12181}, {2800,12438}, {2802,12696}, {2806,12796}, {2829,12113}, {9913,11853}, {10058,11912}, {10074,11913}, {10698,11910}, {11715,11831}, {11832,12138}, {11839,12199}, {11845,12248}, {11848,12332}, {11885,12499}, {11900,12751}, {11901,12753}, {11902,12754}, {11903,12761}, {11904,12762}, {11905,12763}, {11906,12764}, {11907,12765}, {11908,12766}, {11911,12773}, {11914,12775}, {11915,12776}
X(12752) = midpoint of X(153) and X(4240)
X(12752) = X(104)-of-Gossard-triangle
X(12752) = reflection of X(i) in X(j) for these (i,j): (104,402), (1650,119)
The reciprocal orthologic center of these triangles is X(40).
X(12753) lies on these lines: {6,104}, {11,6202}, {100,11824}, {119,5591}, {153,1271}, {515,6263}, {952,1161}, {1317,10927}, {1768,5589}, {2771,7732}, {2783,6319}, {2787,6227}, {2800,3641}, {2802,12697}, {2806,12805}, {2829,5871}, {5595,9913}, {5605,10698}, {5689,12751}, {6215,10742}, {8198,12462}, {8205,12463}, {8216,12765}, {8217,12766}, {9994,12499}, {10040,10058}, {10048,10074}, {10783,12248}, {10792,12199}, {10919,12761}, {10921,12762}, {10923,12763}, {10925,12764}, {10929,12775}, {10931,12776}, {11370,11715}, {11388,12138}, {11497,12332}, {11901,12752}, {11916,12773}
X(12753) = reflection of X(12754) in X(104)
X(12753) = X(104)-of-inner-Grebe-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12754) lies on these lines: {6,104}, {11,6201}, {100,11825}, {119,5590}, {153,1270}, {515,6262}, {952,1160}, {1317,10928}, {1768,5588}, {2771,7733}, {2783,6320}, {2787,6226}, {2800,3640}, {2802,12698}, {2806,12806}, {2829,5870}, {5594,9913}, {5604,10698}, {5688,12751}, {6214,10742}, {8199,12462}, {8206,12463}, {8218,12765}, {8219,12766}, {9995,12499}, {10041,10058}, {10049,10074}, {10784,12248}, {10793,12199}, {10920,12761}, {10922,12762}, {10924,12763}, {10926,12764}, {10930,12775}, {10932,12776}, {11371,11715}, {11389,12138}, {11498,12332}, {11902,12752}, {11917,12773}
X(12754) = reflection of X(12753) in X(104)
X(12754) = X(104)-of-outer-Grebe-triangle
The reciprocal orthologic center of these triangles is X(3869).
X(12755) lies on these lines: {7,80}, {9,12532}, {100,518}, {104,2346}, {390,2800}, {516,11571}, {517,12730}, {952,7672}, {971,10728}, {1156,2771}, {1387,11025}, {1445,6326}, {1768,7675}, {2802,12630}, {2829,12669}, {3868,5856}, {4326,12767}, {5083,11038}, {5809,9809}, {5851,10394}, {6224,7674}, {6264,11526}, {6265,7677}, {7676,12515}, {7678,12611}, {7679,12619}, {8232,12691}, {8236,12758}, {8237,12768}, {8238,12770}, {8385,12759}, {8386,12760}, {8387,12771}, {8389,12774}, {8732,9946}, {9952,10865}, {10889,12551}
X(12755) = reflection of X(i) in X(j) for these (i,j): (7,11570), (1156,5728), (12532,9)
X(12755) = X(265)-of-Honsberger-triangle
X(12755) = excentral-to-Honsberger similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(12757).
X(12756) lies on these lines: {8,6835}, {40,12757}, {191,9898}, {1728,10059}, {3957,12260}, {11224,12654}
X(12756) = reflection of X(12777) in X(12670)
The reciprocal orthologic center of these triangles is X(12756).
X(12757) lies on these lines: {9,48}, {20,2800}, {40,12756}, {65,952}, {80,6826}, {442,12675}, {1768,10268}, {3560,6265}, {3754,5881}, {5204,12738}, {5445,5770}, {5554,9803}, {5693,5731}, {6897,12247}, {9940,12619}
X(12757) = midpoint of X(6224) and X(9964)
X(12757) = reflection of X(i) in X(j) for these (i,j): (80,9946), (12665,6326), (12691,214)
The reciprocal orthologic center of these triangles is X(3869).
X(12758) lies on these lines: {1,104}, {3,10094}, {4,10043}, {8,80}, {11,517}, {12,12611}, {35,214}, {40,10090}, {55,6265}, {56,12515}, {65,1387}, {72,5854}, {90,1320}, {100,997}, {119,10039}, {145,12532}, {153,10935}, {355,12764}, {390,2801}, {392,3035}, {497,10051}, {758,2611}, {946,8068}, {950,12691}, {952,1898}, {960,1145}, {1317,2771}, {1537,12047}, {1697,6326}, {2098,12737}, {2829,12672}, {3036,10914}, {3295,12739}, {3476,12248}, {3586,8275}, {3601,9946}, {3612,3890}, {3753,6667}, {3885,12531}, {3899,5223}, {4294,6224}, {4302,12119}, {4313,9964}, {5252,10742}, {5531,9819}, {5533,10265}, {5730,8668}, {5919,12735}, {6264,7962}, {6702,7741}, {8071,12332}, {8236,12755}, {8239,12768}, {8240,12770}, {8241,12771}, {8390,12759}, {8392,12760}, {9668,12747}, {9785,9803}, {9952,10866}, {10284,10950}, {10738,12701}, {11924,12774}, {12647,12751}
X(12758) = midpoint of X(i) and X(j) for these {i,j}: {80,5697}, {145,12532}, {1320,3869}, {3885,12531}
X(12758) = reflection of X(i) in X(j) for these (i,j): (65,1387), (214,3884), (1145,960), (1317,9957), (10914,3036), (11570,1), (11571,5083), (12665,5887)
X(12758) = X(265)-of-Hutson-intouch-triangle
X(12758) = X(12121)-of-intouch-triangle
X(12758) = excentral-to-Hutson-intouch similarity image of X(6326)
X(12758) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1768,10074), (1,11571,5083), (497,12247,10073), (1697,6326,10087), (5083,11571,11570), (10265,12053,5533)
The reciprocal orthologic center of these triangles is X(3869).
X(12759) lies on these lines: {363,6326}, {517,12733}, {1387,11026}, {1768,8111}, {2800,9836}, {2802,12633}, {5083,11039}, {5934,12691}, {6264,11527}, {6265,8109}, {8107,12515}, {8113,11570}, {8133,12771}, {8140,12760}, {8377,12611}, {8380,12619}, {8385,12755}, {8390,12758}, {8391,12770}, {9783,9803}, {9946,11854}, {9952,11856}, {9964,11886}, {11685,12532}, {11892,12551}, {11922,12768}
X(12759) = reflection of X(12760) in X(12767)
X(12759) = X(265)-of-inner-Hutson-triangle
X(12759) = excentral-to-inner-Hutson similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3869).
X(12760) lies on these lines: {517,12734}, {1387,11027}, {1768,8112}, {2800,9837}, {2802,12634}, {5083,11040}, {5935,12691}, {6264,11528}, {6265,8110}, {8108,12515}, {8114,11570}, {8135,12771}, {8140,12759}, {8378,12611}, {8381,12619}, {8386,12755}, {8392,12758}, {9946,11855}, {9952,11857}, {9964,11887}, {11686,12532}, {11893,12551}, {11925,12768}, {11926,12770}
X(12760) = reflection of X(12759) in X(12767)
X(12760) = X(265)-of-outer-Hutson-triangle
X(12760) = excentral-to-outer-Hutson similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(40).
X(12761) lies on these lines: {4,11}, {12,12775}, {80,6001}, {100,11826}, {119,1376}, {149,12667}, {153,3434}, {355,2800}, {515,10738}, {952,6256}, {1012,8068}, {1158,12619}, {1317,10947}, {1478,1537}, {1519,12740}, {1532,10090}, {1768,10826}, {2787,12182}, {2802,12700}, {2950,5587}, {3035,6850}, {3419,12665}, {3585,10057}, {4996,6932}, {5840,11500}, {5842,10724}, {6265,12608}, {6667,6893}, {6713,6929}, {7971,9897}, {9913,10829}, {10058,10523}, {10074,10948}, {10698,10944}, {10794,12199}, {10871,12499}, {10914,12751}, {10919,12753}, {10920,12754}, {10945,12765}, {10946,12766}, {10949,12776}, {11373,11715}, {11390,12138}, {11865,12462}, {11866,12463}, {11903,12752}, {11928,12773}
X(12761) = midpoint of X(i) and X(j) for these {i,j}: {149,12667}, {7971,9897}
X(12761) = reflection of X(i) in X(j) for these (i,j): (1158,12619), (6265,12608), (12114,11), (12332,119), (12762,10742)
X(12761) = X(104)-of-inner-Johnson-triangle
X(12761) = {X(4), X(104)}-harmonic conjugate of X(12764)
The reciprocal orthologic center of these triangles is X(40).
X(12762) lies on these lines: {11,10532}, {12,104}, {20,100}, {72,12751}, {80,7686}, {119,958}, {355,2800}, {515,12738}, {952,10526}, {1317,10806}, {1768,10827}, {2787,12183}, {2802,5812}, {2886,6982}, {4295,12247}, {4298,10265}, {4301,10738}, {5220,5690}, {5270,11219}, {5432,12115}, {6253,10728}, {9913,10830}, {10058,10954}, {10074,10523}, {10698,10950}, {10786,12248}, {10795,12199}, {10872,12499}, {10921,12753}, {10922,12754}, {10951,12765}, {10952,12766}, {10955,12775}, {11236,12114}, {11374,11715}, {11391,12138}, {11867,12462}, {11868,12463}, {11904,12752}, {11929,12773}
X(12762) = reflection of X(12761) in X(10742)
X(12762) = X(104)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12763) lies on the Johnson-Yff-inner circle and these lines: {1,10742}, {4,1317}, {5,10074}, {11,153}, {12,104}, {30,10087}, {55,2829}, {56,119}, {65,12751}, {80,942}, {100,7354}, {149,5229}, {355,11570}, {495,10058}, {515,12739}, {952,1478}, {1388,11729}, {1466,9657}, {1479,12735}, {1537,2098}, {1768,9578}, {1836,2802}, {1837,5083}, {2771,10057}, {2800,5252}, {3032,9553}, {3035,3436}, {3045,9653}, {3085,12248}, {3585,7972}, {5434,10711}, {5541,9579}, {5691,12743}, {6264,9612}, {6284,10728}, {6326,9613}, {8068,9654}, {9655,12331}, {9913,10831}, {10039,12515}, {10090,11698}, {10106,12740}, {10404,12736}, {10698,10944}, {10797,12199}, {10827,12619}, {10873,12499}, {10923,12753}, {10924,12754}, {10957,12776}, {11375,11715}, {11392,12138}, {11501,12332}, {11869,12462}, {11870,12463}, {11905,12752}, {11930,12765}, {11931,12766}, {12047,12737}
X(12763) = reflection of X(i) in X(j) for these (i,j): (55,10956), (10058,495)
X(12763) = X(104)-of-1st-Johnson-Yff-triangle
X(12763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10742,12764), (153,388,11), (3585,7972,10738), (9654,12773,8068)
The reciprocal orthologic center of these triangles is X(40).
X(12764) lies on the Johnson-Yff-outer circle and these lines: {1,10742}, {4,11}, {5,10058}, {30,10090}, {55,119}, {80,517}, {100,1329}, {149,3436}, {153,497}, {355,12758}, {377,6667}, {381,8068}, {480,528}, {496,10074}, {515,12740}, {529,10707}, {950,12739}, {952,1479}, {1156,11604}, {1319,1538}, {1320,5080}, {1387,1478}, {1388,6256}, {1532,5172}, {1537,2099}, {1737,12515}, {1768,9581}, {1836,12736}, {1837,2800}, {1898,2771}, {2475,6691}, {2478,3035}, {2787,12185}, {2802,12701}, {2841,10774}, {3032,9554}, {3036,3434}, {3045,9666}, {3057,12751}, {3058,10711}, {3303,10956}, {3586,6326}, {4186,9672}, {4857,7972}, {4996,11114}, {5432,6965}, {5533,9669}, {5541,9580}, {5722,11570}, {5840,6928}, {6264,9614}, {6265,10572}, {6713,6923}, {6840,10724}, {9668,12331}, {9670,10953}, {9913,10832}, {9957,12749}, {10087,11698}, {10698,10950}, {10798,12199}, {10826,12619}, {10874,12499}, {10925,12753}, {10926,12754}, {10958,12775}, {10959,12776}, {11376,11715}, {11393,12138}, {11502,12332}, {11871,12462}, {11872,12463}, {11906,12752}, {11932,12765}, {11933,12766}
X(12764) = midpoint of X(149) and X(3436)
X(12764) = reflection of X(i) in X(j) for these (i,j): (56,11), (100,1329), (10074,496)
X(12764) = X(104)-of-2nd-Johnson-Yff-triangle
X(12764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,10742,12763), (80,3583,10738), (153,497,1317), (9669,12773,5533)
The reciprocal orthologic center of these triangles is X(40).
X(12765) lies on these lines: {11,8212}, {100,11828}, {104,493}, {119,8222}, {153,6462}, {515,12741}, {952,10669}, {1317,11947}, {1768,8188}, {2787,12186}, {2800,12440}, {2829,9838}, {6461,12766}, {8194,9913}, {8201,12462}, {8208,12463}, {8210,10698}, {8214,12751}, {8216,12753}, {8218,12754}, {8220,10742}, {10058,11951}, {10074,11953}, {10875,12499}, {11377,11715}, {11394,12138}, {11503,12332}, {11840,12199}, {11846,12248}, {11930,12763}, {11932,12764}, {11949,12773}, {11955,12775}, {11957,12776}
X(12765) = X(104)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12766) lies on these lines: {11,8213}, {100,11829}, {104,494}, {119,8223}, {153,6463}, {515,12742}, {952,10673}, {1317,11948}, {1768,8189}, {2787,12187}, {2800,12441}, {2829,9839}, {6461,12765}, {8195,9913}, {8202,12462}, {8209,12463}, {8211,10698}, {8215,12751}, {8217,12753}, {8219,12754}, {8221,10742}, {10058,11952}, {10074,11954}, {10876,12499}, {11378,11715}, {11395,12138}, {11504,12332}, {11841,12199}, {11847,12248}, {11931,12763}, {11933,12764}, {11950,12773}, {11956,12775}, {11958,12776}
X(12766) = X(104)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(3869).
X(12767) lies on these lines: {1,104}, {10,9809}, {11,3339}, {40,2771}, {80,2093}, {100,3984}, {149,9589}, {153,3679}, {165,6326}, {200,12532}, {484,6001}, {516,9803}, {517,7993}, {952,7991}, {971,3245}, {1145,5223}, {1317,9819}, {1387,10980}, {1537,11219}, {1699,10265}, {1709,3065}, {1750,12691}, {2717,2958}, {2801,2951}, {2802,11519}, {2829,7992}, {3337,12672}, {4326,12755}, {4668,12751}, {4674,9355}, {5010,12332}, {5691,12247}, {5732,9964}, {6264,11531}, {6265,7987}, {7280,7971}, {7972,7990}, {7982,12773}, {7988,12611}, {7989,12619}, {8089,12771}, {8140,12759}, {8244,12768}, {8245,12770}, {8423,12774}, {9946,10857}, {10045,10057}, {10073,10092}, {10970,12749}, {10971,12750}, {11224,12737}, {11280,12114}
X(12767) = midpoint of X(12759) and X(12760)
X(12767) = reflection of X(i) in X(j) for these (i,j): (1,1768), (5531,40), (5691,12247), (6326,12515), (7982,12773), (9589,149), (9809,10), (11531,6264)
X(12767) = X(265)-of-6th-mixtilinear-triangle
X(12767) = excentral-to-6th-mixtilinear similarity image of X(6326)
X(12767) = {X(6326), X(12515)}-harmonic conjugate of X(165)
The reciprocal orthologic center of these triangles is X(3869).
X(12768) lies on these lines: {80,7595}, {104,7133}, {517,12744}, {952,9808}, {1387,11030}, {1768,8234}, {2771,12490}, {2800,7596}, {2802,12638}, {2829,12681}, {5083,11042}, {6264,11532}, {6265,8225}, {6326,8231}, {8224,12515}, {8228,12611}, {8230,12619}, {8233,12691}, {8237,12755}, {8239,12758}, {8243,11570}, {8244,12767}, {8246,12770}, {9789,9803}, {9946,10858}, {9952,10867}, {9964,10885}, {10265,12610}, {10891,12551}, {11687,12532}, {11996,12774}
X(12768) = X(265)-of-2nd-Pamfilos-Zhou-triangle
X(12768) = excentral-to-2nd-Pamfilos-Zhou similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3065).
X(12769) lies on these lines: {8,12535}, {90,6599}, {191,12409}, {1657,5693}, {1836,6763}, {2476,3336}
X(12769) = reflection of X(i) in X(j) for these (i,j): (12409,191), (12786,12682)
X(12769) = X(6595)-of-inner-Garcia-triangle
The reciprocal orthologic center of these triangles is X(3869).
X(12770) lies on these lines: {5,3120}, {21,104}, {80,256}, {517,12746}, {846,6326}, {952,2292}, {1284,11570}, {1387,11031}, {1768,8235}, {2800,9840}, {2802,12642}, {2829,12683}, {4199,12691}, {4220,12515}, {4425,10265}, {5051,12619}, {5083,11043}, {6264,11533}, {8229,12611}, {8238,12755}, {8240,12758}, {8245,12767}, {8246,12768}, {8249,12771}, {8391,12759}, {8425,12774}, {8731,9946}, {9791,9803}, {9952,10868}, {10892,12551}, {11688,12532}, {11926,12760}
X(12770) = X(265)-of-1st-Sharygin-triangle
X(12770) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13277)
X(12770) = excentral-to-1st-Sharygin similarity image of X(6326)
X(12770) = hexyl-to-1st-Sharygin similarity image of X(1768)
The reciprocal orthologic center of these triangles is X(3869).
X(12771) lies on these lines: {1,12772}, {517,8097}, {952,8093}, {1387,11032}, {1768,8081}, {2089,11570}, {2771,8099}, {2800,8091}, {2829,8095}, {6265,8077}, {6326,8078}, {8075,12515}, {8079,12691}, {8085,12611}, {8087,12619}, {8089,12767}, {8133,12759}, {8135,12760}, {8241,12758}, {8247,12768}, {8249,12770}, {8387,12755}, {8733,9946}, {9793,9803}, {9964,11888}, {11690,12532}, {11894,12551}
X(12771) = reflection of X(12772) in X(1)
X(12771) = X(265)-of-tangential-midarc-triangle
X(12771) = X(12898)-of-2nd-tangential-midarc-triangle
X(12771) = excentral-to-tangential-midarc similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(3869).
X(12772) lies on these lines: {1,12771}, {174,11570}, {258,6326}, {1387,11033}, {2802,12644}, {5083,8351}, {6264,11899}, {6265,7588}, {8125,12532}, {8734,9946}, {9952,11859}, {11895,12551}
X(12772) = reflection of X(12771) in X(1)
X(12772) = X(265)-of-2nd-tangential-midarc-triangle
X(12772) = X(12898)-of-tangential-midarc-triangle
X(12772) = excentral-to-2nd-tangential-midarc similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(40).
X(12773) lies on the Stammler circle and these lines: {1,399}, {2,11698}, {3,8}, {4,1484}, {5,153}, {11,381}, {30,149}, {36,9897}, {40,7993}, {55,7972}, {56,80}, {57,6797}, {119,1656}, {214,958}, {355,10265}, {382,2829}, {515,12747}, {517,1768}, {528,3534}, {993,3655}, {1001,2801}, {1012,10247}, {1317,3295}, {1320,8148}, {1385,5251}, {1387,3485}, {1482,2800}, {1483,6906}, {1537,10941}, {1597,1862}, {1598,12138}, {1657,5840}, {2099,11571}, {2787,12188}, {2802,11256}, {2830,11258}, {3032,9566}, {3035,5054}, {3036,9709}, {3045,9703}, {3243,3358}, {3304,12611}, {3359,11525}, {3428,12119}, {3526,6713}, {3576,5531}, {3579,3893}, {3652,3884}, {3830,10707}, {4413,5790}, {4428,11274}, {5055,10711}, {5073,10724}, {5093,10759}, {5450,11849}, {5533,9669}, {5603,9809}, {5708,12736}, {5730,12532}, {5844,6909}, {6361,9802}, {6767,12735}, {6862,10805}, {6912,10283}, {6913,11729}, {6914,7967}, {6971,10785}, {6980,12115}, {7517,9913}, {7982,12767}, {8068,9654}, {9301,12499}, {10966,12743}, {11492,12461}, {11493,12460}, {11842,12199}, {11875,12462}, {11876,12463}, {11911,12752}, {11916,12753}, {11917,12754}, {11928,12761}, {11929,12762}, {11949,12765}, {11950,12766}, {12000,12775}
X(12773) = midpoint of X(i) and X(j) for these {i,j}: {40,7993}, {149,12248}, {944,9803}, {1768,6264}, {6361,9802}, {7982,12767}
X(12773) = reflection of X(i) in X(j) for these (i,j): (3,104), (4,1484), (153,5), (355,10265), (382,10738), (1482,12737), (3830,10707), (5073,10724), (5541,3579), (5790,11219), (6265,11715), (6326,1385), (8148,1320), (10742,11), (12331,3), (12332,5450), (12702,12515), (12738,214), (12751,12619)
X(12773) = anticomplement of X(11698)
X(12773) = antipode of X(12331) in Stammler circle
X(12773) = X(104)-of-X3-ABC-reflections-triangle
X(12773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11,10074,999), (11,10742,381), (1317,10058,3295), (5533,12764,9669), (6265,11715,10246), (8068,12763,9654)
The reciprocal orthologic center of these triangles is X(3869).
X(12774) lies on these lines: {174,11570}, {517,12748}, {952,12445}, {1387,8083}, {2771,12491}, {2800,8351}, {2802,12646}, {2829,12685}, {6264,11535}, {6265,7587}, {8126,12532}, {8382,12619}, {8423,12767}, {8425,12770}, {8729,9946}, {9803,11891}, {9952,11860}, {9964,11890}, {11896,12551}, {11924,12758}, {11996,12768}
X(12774) = X(265)-of-Yff-central-triangle
X(12774) = excentral-to-Yff-central similarity image of X(6326)
The reciprocal orthologic center of these triangles is X(40).
X(12775) lies on these lines: {1,104}, {3,1537}, {4,100}, {11,6833}, {12,12761}, {35,12608}, {55,2829}, {56,11047}, {149,6847}, {153,10528}, {515,10087}, {516,1519}, {946,10090}, {952,1012}, {962,4996}, {1006,3359}, {1145,10306}, {1317,10965}, {1376,6968}, {1470,5603}, {1512,5537}, {1621,6950}, {2787,12189}, {2802,12703}, {3035,6834}, {3295,10935}, {3560,5554}, {3601,11919}, {3811,12665}, {4302,6256}, {5528,11372}, {6001,12739}, {6265,12672}, {6326,12705}, {6713,6977}, {6831,10738}, {6935,10596}, {9913,10834}, {10073,12616}, {10742,10942}, {10803,12199}, {10805,12248}, {10878,12499}, {10915,12751}, {10929,12753}, {10930,12754}, {10955,12762}, {10958,12764}, {11400,12138}, {11881,12462}, {11882,12463}, {11914,12752}, {11955,12765}, {11956,12766}, {12000,12773}
X(12775) = reflection of X(i) in X(j) for these (i,j): (104,10058), (12115,10956)
X(12775) = X(104)-of-inner-Yff-tangents-triangle
X(12775) = {X(104),X(10698)}-harmonic conjugate of X(12776)
X(12775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (119,11248,100), (5450,10074,104), (6906,10698,104)
The reciprocal orthologic center of these triangles is X(40).
X(12776) lies on these lines: {1,104}, {4,10707}, {11,10532}, {72,6265}, {100,6942}, {119,10527}, {153,10529}, {411,10031}, {515,12750}, {519,6905}, {528,6934}, {952,3149}, {1317,10966}, {1537,10941}, {2787,12190}, {2802,12704}, {2829,12116}, {3058,6938}, {3304,6833}, {3829,6968}, {4848,10090}, {4996,6585}, {5288,5660}, {6326,6762}, {6830,10072}, {6834,12513}, {6941,10711}, {6956,10597}, {9851,10971}, {9913,10835}, {10742,10943}, {10804,12199}, {10806,12248}, {10879,12499}, {10916,12751}, {10931,12753}, {10932,12754}, {10949,12761}, {10957,12763}, {10959,12764}, {11401,12138}, {11510,12332}, {11883,12462}, {11884,12463}, {11915,12752}, {11957,12765}, {11958,12766}
X(12776) = reflection of X(104) in X(10074)
X(12776) = X(104)-of-outer-Yff-tangents-triangle
X(12776) = {X(104),X(10698)}-harmonic conjugate of X(12775)
The reciprocal orthologic center of these triangles is X(40).
X(12777) lies on these lines: {1,12521}, {2,12260}, {4,5223}, {8,6835}, {10,6601}, {40,4847}, {100,3523}, {354,12439}, {497,10395}, {515,12120}, {518,12692}, {519,8000}, {942,2550}, {1737,10075}, {2551,12019}, {3295,6675}, {3419,12667}, {3434,11684}, {3679,9898}, {3873,12537}, {5090,12139}, {5587,12599}, {5657,12249}, {5687,12333}, {5688,12802}, {5689,12801}, {6737,11525}, {6743,6864}, {8193,12411}, {8197,12464}, {8204,12465}, {9804,11024}, {9857,12500}, {10039,10059}, {10791,12200}, {11900,12789}
X(12777) = midpoint of X(8) and X(9874)
X(12777) = reflection of X(i) in X(j) for these (i,j): (7160,10), (12756,12670)
X(12777) = anticomplement of X(12260)
X(12777) = X(7160)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12778) lies on these lines: {1,1511}, {2,12261}, {3,11709}, {8,12383}, {10,265}, {30,12368}, {35,1807}, {40,2940}, {46,3028}, {65,5504}, {72,74}, {110,517}, {113,12699}, {146,6361}, {165,12041}, {399,12702}, {484,4551}, {515,12121}, {516,7728}, {542,3416}, {1155,10081}, {1385,7984}, {1482,11720}, {1770,12373}, {2777,12779}, {2778,9934}, {2836,11579}, {3057,10091}, {3448,5657}, {3656,5642}, {3679,12407}, {5090,12140}, {5183,11670}, {5587,10113}, {5609,7991}, {5687,12334}, {5688,12804}, {5689,12803}, {5690,12785}, {5886,5972}, {7727,11010}, {7968,10820}, {7969,10819}, {8193,12412}, {8197,12466}, {8204,12467}, {9778,12244}, {9857,12501}, {10778,12619}, {10791,12201}, {11900,12790}
X(12778) = midpoint of X(i) and X(j) for these {i,j}: {8,12383}, {40,2948}, {146,6361}, {399,12702}
X(12778) = reflection of X(i) in X(j) for these (i,j): (1,1511), (74,3579), (265,10), (1482,11720), (3656,5642), (7978,11699), (7984,1385), (10778,12619), (12699,113)
X(12778) = anticomplement of X(12261)
X(12778) = X(265)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12779) lies on these lines: {1,2883}, {2,12262}, {4,65}, {8,6225}, {10,64}, {30,9928}, {154,4297}, {165,5894}, {221,950}, {226,1854}, {355,6000}, {440,12520}, {515,1498}, {516,5895}, {517,5878}, {519,7973}, {607,5776}, {944,5656}, {1103,1490}, {1503,3751}, {1698,6696}, {1699,5893}, {1712,8899}, {1737,10076}, {2192,10106}, {2777,12778}, {3197,8804}, {3556,7580}, {3679,9899}, {5090,11381}, {5252,6285}, {5587,6247}, {5657,12250}, {5687,12335}, {5688,6266}, {5689,6267}, {6684,10606}, {7522,12617}, {7987,10192}, {8193,9914}, {8197,12468}, {8204,12469}, {8567,10164}, {9857,12502}, {10039,10060}, {10791,12202}, {11900,12791}
X(12779) = midpoint of X(8) and X(6225)
X(12779) = reflection of X(i) in X(j) for these (i,j): (1,2883), (64,10)
X(12779) = anticomplement of X(12262)
X(12779) = X(64)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12780) lies on these lines: {1,619}, {2,11706}, {8,617}, {10,14}, {40,2946}, {515,5474}, {517,5613}, {519,5464}, {530,9881}, {531,3679}, {542,3416}, {1018,1276}, {1698,6670}, {1737,10077}, {5090,12141}, {5470,11599}, {5479,5587}, {5657,6773}, {5687,12336}, {5688,6269}, {5689,6271}, {7975,11711}, {7983,11705}, {8193,9915}, {8197,12470}, {8204,12471}, {9857,9981}, {10039,10061}, {10791,12204}, {11900,12792}
X(12780) = midpoint of X(8) and X(617)
X(12780) = reflection of X(i) in X(j) for these (i,j): (1,619), (14,10), (7975,11711), (7983,11705)
X(12780) = X(14)-of-outer-Garcia-triangle
X(12780) = {X(3416),X(3654)}-harmonic conjugate of X(12781)
The reciprocal orthologic center of these triangles is X(3).
X(12781) lies on these lines: {1,618}, {2,11705}, {8,616}, {10,13}, {40,2945}, {515,5473}, {517,5617}, {519,5463}, {530,3679}, {531,9881}, {542,3416}, {1018,1277}, {1698,6669}, {1737,10078}, {5090,12142}, {5469,11599}, {5478,5587}, {5657,6770}, {5687,12337}, {5688,6268}, {5689,6270}, {7974,11711}, {7983,11706}, {8193,9916}, {8197,12472}, {8204,12473}, {9857,9982}, {10039,10062}, {10791,12205}, {11900,12793}
X(12781) = midpoint of X(8) and X(616)
X(12781) = reflection of X(i) in X(j) for these (i,j): (1,618), (13,10), (7974,11711), (7983,11706)
X(12781) = X(13)-of-outer-Garcia-triangle
X(12781) = {X(3416),X(3654)}-harmonic conjugate of X(12780)
The reciprocal orthologic center of these triangles is X(3).
X(12782) lies on these lines: {1,39}, {2,12263}, {3,11364}, {6,12194}, {8,194}, {10,75}, {37,4446}, {38,3661}, {40,511}, {99,12195}, {165,5188}, {190,3764}, {192,3778}, {238,3730}, {256,3729}, {262,946}, {274,4476}, {355,2782}, {384,10791}, {515,11257}, {517,3095}, {518,3094}, {519,7757}, {536,4443}, {538,3679}, {712,4424}, {732,3416}, {734,4680}, {736,4769}, {944,7709}, {982,3912}, {985,5280}, {1125,7786}, {1385,11171}, {1469,3503}, {1582,2273}, {1698,3934}, {1700,12021}, {1701,12020}, {1737,10079}, {1740,3688}, {1757,3496}, {2664,4517}, {3122,4664}, {3579,9821}, {3624,6683}, {4642,4712}, {4649,5145}, {4669,11055}, {5007,10789}, {5090,12143}, {5587,6248}, {5657,12251}, {5687,12338}, {5688,6272}, {5689,6273}, {5886,11272}, {5969,9881}, {7697,9956}, {7772,10800}, {8193,9917}, {8197,12474}, {8204,12475}, {8298,8715}, {9857,9983}, {10039,10063}, {11900,12794}
X(12782) = midpoint of X(8) and X(194)
X(12782) = reflection of X(i) in X(j) for these (i,j): (1,39), (76,10), (4443,4735), (9821,3579)
X(12782) = anticomplement of X(12263)
X(12782) = X(76)-of-outer-Garcia-triangle
X(12782) = {X(1), X(3097)}-harmonic conjugate of X(39)
The reciprocal orthologic center of these triangles is X(3).
X(12783) lies on these lines: {1,6292}, {2,12264}, {8,2896}, {10,82}, {515,12122}, {517,6287}, {519,7977}, {732,3416}, {754,3679}, {1018,3496}, {1698,6704}, {1737,10080}, {3579,8725}, {4745,12156}, {5090,12144}, {5587,6249}, {5657,12252}, {5687,12339}, {5688,6274}, {5689,6275}, {5690,9864}, {6308,11364}, {6684,9751}, {8193,9918}, {8197,12476}, {8204,12477}, {10039,10064}, {10791,12206}, {11900,12795}
X(12783) = midpoint of X(8) and X(2896)
X(12783) = reflection of X(i) in X(j) for these (i,j): (1,6292), (83,10), (8725,3579)
X(12783) = anticomplement of X(12264)
X(12783) = X(83)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12784) lies on these lines: {1,132}, {2,12265}, {8,12384}, {10,1297}, {80,2831}, {112,515}, {127,5587}, {944,11722}, {946,10705}, {1837,3320}, {2794,5691}, {2799,9864}, {2806,12751}, {3576,6720}, {3679,9530}, {5090,12145}, {5252,6020}, {5657,12253}, {5687,12340}, {5688,12806}, {5689,12805}, {8193,12413}, {8197,12478}, {8204,12479}, {9517,12368}, {9857,12503}, {10791,12207}, {11900,12796}
X(12784) = midpoint of X(8) and X(12384)
X(12784) = reflection of X(i) in X(j) for these (i,j): (1,132), (944,11722), (1297,10), (10705,946)
X(12784) = anticomplement of X(12265)
X(12784) = X(1297)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12785) lies on these lines: {1,1209}, {2,12266}, {8,2888}, {10,54}, {65,2962}, {72,6145}, {80,6286}, {195,5790}, {355,1154}, {515,7691}, {517,6288}, {519,7979}, {539,3679}, {1698,6689}, {1737,10082}, {3468,4551}, {3574,5587}, {3751,5965}, {5090,11576}, {5657,12254}, {5687,12341}, {5688,6276}, {5689,6277}, {5690,12778}, {8193,9920}, {8197,12480}, {8204,12481}, {9857,9985}, {10039,10066}, {10628,12368}, {10791,12208}, {11900,12797}
X(12785) = midpoint of X(8) and X(2888)
X(12785) = reflection of X(i) in X(j) for these (i,j): (1,1209), (54,10)
X(12785) = anticomplement of X(12266)
X(12785) = X(54)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12786) lies on these lines: {1,6597}, {2,12267}, {8,12535}, {10,10266}, {100,191}, {2802,6595}, {3679,12409}, {5090,12146}, {5538,5694}, {5587,12600}, {5657,12255}, {5687,12342}, {5688,12808}, {5689,12807}, {8193,12414}, {8197,12482}, {8204,12483}, {9857,12504}, {10791,12209}, {11024,12543}, {11900,12798}
X(12786) = reflection of X(i) in X(j) for these (i,j): (6597,12745), (10266,10), (12769,12682)
X(12786) = anticomplement of X(12267)
X(12786) = X(10266)-of-outer-Garcia-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12787) lies on these lines: {1,642}, {2,12268}, {8,487}, {10,486}, {515,12123}, {517,6290}, {519,7980}, {1018,6212}, {1698,6119}, {1737,10083}, {3416,3564}, {3617,12221}, {3679,9906}, {5090,12147}, {5587,6251}, {5657,12256}, {5687,12343}, {5688,6280}, {5689,6281}, {5790,12601}, {8193,9921}, {8197,12484}, {8204,12485}, {9857,9986}, {10039,10067}, {10791,12210}, {11900,12799}
X(12787) = midpoint of X(8) and X(487)
X(12787) = reflection of X(i) in X(j) for these (i,j): (1,642), (486,10)
X(12787) = anticomplement of X(12268)
X(12787) = X(486)-of-outer-Garcia-triangle
X(12787) = {X(3416),X(5690)}-harmonic conjugate of X(12788)
The reciprocal orthologic center of these triangles is X(3).
X(12788) lies on these lines: {1,641}, {2,12269}, {8,488}, {10,485}, {515,12124}, {517,6289}, {519,7981}, {1018,6213}, {1698,6118}, {1737,10084}, {3416,3564}, {3617,12222}, {3679,9907}, {5090,12148}, {5587,6250}, {5657,12257}, {5687,12344}, {5688,6278}, {5689,6279}, {5790,12602}, {8193,9922}, {8197,12486}, {8204,12487}, {9857,9987}, {10039,10068}, {10791,12211}, {11900,12800}
X(12788) = midpoint of X(8) and X(488)
X(12788) = reflection of X(i) in X(j) for these (i,j): (1,641), (485,10)
X(12788) = anticomplement of X(12269)
X(12788) = X(485)-of-outer-Garcia-triangle
X(12788) = {X(3416),X(5690)}-harmonic conjugate of X(12787)
The reciprocal orthologic center of these triangles is X(40).
X(12789) lies on these lines: {30,12120}, {402,7160}, {4240,9874}, {8000,11910}, {9898,11852}, {10059,11912}, {10075,11913}, {11831,12260}, {11832,12139}, {11839,12200}, {11845,12249}, {11848,12333}, {11853,12411}, {11885,12500}, {11897,12599}, {11900,12777}, {11901,12801}, {11902,12802}
X(12789) = midpoint of X(4240) and X(9874)
X(12789) = reflection of X(7160) in X(402)
X(12789) = X(10266)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12790) lies on these lines: {30,110}, {265,402}, {542,12583}, {1511,1650}, {2771,12729}, {2777,12791}, {3448,11845}, {4240,12383}, {5663,12113}, {10088,11905}, {10091,11906}, {10113,11897}, {11831,12261}, {11832,12140}, {11839,12201}, {11848,12334}, {11852,12407}, {11853,12412}, {11885,12501}, {11900,12778}, {11901,12803}, {11902,12804}
X(12790) = midpoint of X(4240) and X(12383)
X(12790) = X(265)-of-Gossard-triangle
X(12790) = reflection of X(i) in X(j) for these (i,j): (265,402), (1650,1511)
The reciprocal orthologic center of these triangles is X(4).
X(12791) lies on these lines: {30,155}, {64,402}, {1650,2883}, {2777,12790}, {4240,6225}, {5502,12113}, {6000,11251}, {6001,12696}, {6247,11897}, {6266,11902}, {6267,11901}, {7355,11909}, {7973,11910}, {9899,11852}, {9914,11853}, {10060,11912}, {10076,11913}, {11381,11832}, {11831,12262}, {11839,12202}, {11845,12250}, {11848,12335}, {11885,12502}, {11900,12779}
X(12791) = midpoint of X(4240) and X(6225)
X(12791) = reflection of X(i) in X(j) for these (i,j): (64,402), (1650,2883)
X(12791) = X(64)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12792) lies on these lines: {30,5464}, {530,12347}, {531,1651}, {542,12583}, {617,4240}, {619,1650}, {5479,11897}, {6269,11902}, {6271,11901}, {6773,11845}, {7974,11910}, {9900,11852}, {9915,11853}, {9981,11885}, {10061,11912}, {10077,11913}, {11706,11831}, {11832,12141}, {11839,12204}, {11848,12336}, {11900,12780}
X(12792) = X(14)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12793) lies on these lines: {30,5463}, {530,1651}, {531,12347}, {542,12583}, {616,4240}, {618,1650}, {5478,11897}, {6268,11902}, {6270,11901}, {6770,11845}, {7975,11910}, {9901,11852}, {9916,11853}, {9982,11885}, {10062,11912}, {10078,11913}, {11705,11831}, {11832,12142}, {11839,12205}, {11848,12337}, {11900,12781}
X(12793) = X(13)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12794) lies on these lines: {30,3095}, {39,1650}, {76,402}, {194,4240}, {384,11839}, {511,12113}, {538,1651}, {730,12438}, {732,12583}, {2782,11251}, {5969,12347}, {6248,11897}, {6272,11902}, {6273,11901}, {7976,11910}, {9902,11852}, {9917,11853}, {9983,11885}, {10063,11912}, {10079,11913}, {11831,12263}, {11832,12143}, {11845,12251}, {11848,12338}, {11863,12474}, {11864,12475}, {11900,12782}
X(12794) = midpoint of X(194) and X(4240)
X(12794) = X(76)-of-Gossard-triangle
X(12794) = reflection of X(i) in X(j) for these (i,j): (76,402), (1650,39)
The reciprocal orthologic center of these triangles is X(3).
X(12795) lies on these lines: {30,6287}, {83,402}, {732,12583}, {754,1651}, {1650,6292}, {2896,4240}, {6249,11897}, {6274,11902}, {6275,11901}, {7977,11910}, {9903,11852}, {9918,11853}, {10064,11912}, {10080,11913}, {11831,12264}, {11832,12144}, {11839,12206}, {11845,12252}, {11848,12339}, {11863,12476}, {11864,12477}, {11900,12783}
X(12795) = midpoint of X(2896) and X(4240)
X(12795) = reflection of X(i) in X(j) for these (i,j): (83,402), (1650,6292)
X(12795) = X(83)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12796) lies on these lines: {30,112}, {127,11897}, {132,1650}, {402,1297}, {1651,9530}, {2799,12181}, {2806,12752}, {3320,11909}, {4240,12384}, {9517,12369}, {11831,12265}, {11832,12145}, {11839,12207}, {11845,12253}, {11848,12340}, {11852,12408}, {11853,12413}, {11885,12503}, {11900,12784}, {11901,12805}, {11902,12806}
X(12796) = midpoint of X(4240) and X(12384)
X(12796) = reflection of X(i) in X(j) for these (i,j): (1297,402), (1650,132)
X(12796) = X(1297)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12797) lies on these lines: {30,6288}, {54,402}, {195,11911}, {539,1651}, {1154,11251}, {1209,1650}, {2888,4240}, {3574,11897}, {6276,11902}, {6277,11901}, {7979,11910}, {9905,11852}, {9920,11853}, {9985,11885}, {10066,11912}, {10082,11913}, {10628,12369}, {11576,11832}, {11831,12266}, {11839,12208}, {11845,12254}, {11848,12341}, {11900,12785}
X(12797) = midpoint of X(2888) and X(4240)
X(12797) = reflection of X(i) in X(j) for these (i,j): (54,402), (1650,1209)
X(12797) = X(54)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12798) lies on these lines: {402,10266}, {11831,12267}, {11832,12146}, {11839,12209}, {11845,12255}, {11848,12342}, {11852,12409}, {11853,12414}, {11885,12504}, {11897,12600}, {11900,12786}, {11901,12807}, {11902,12808}
X(12798) = reflection of X(10266) in X(402)
The reciprocal orthologic center of these triangles is X(3).
X(12799) lies on these lines: {30,6290}, {402,486}, {487,4240}, {642,1650}, {3564,12418}, {6251,11897}, {6280,11902}, {6281,11901}, {7980,11910}, {9906,11852}, {9921,11853}, {9986,11885}, {10067,11912}, {10083,11913}, {11831,12268}, {11832,12147}, {11839,12210}, {11845,12256}, {11848,12343}, {11863,12484}, {11864,12485}, {11900,12787}, {11911,12601}
X(12799) = X(486)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(3).
X(12800) lies on these lines: {30,6289}, {402,485}, {488,4240}, {641,1650}, {3564,12418}, {6250,11897}, {6278,11902}, {6279,11901}, {7981,11910}, {9907,11852}, {9922,11853}, {9987,11885}, {10068,11912}, {10084,11913}, {11831,12269}, {11832,12148}, {11845,12257}, {11848,12344}, {11863,12486}, {11864,12487}, {11900,12788}, {11911,12602}
X(12800) = X(485)-of-Gossard-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12801) lies on these lines: {6,7160}, {1271,9874}, {5589,9898}, {5595,12411}, {5605,8000}, {5689,12777}, {6202,12599}, {8198,12464}, {8205,12465}, {9994,12500}, {10040,10059}, {10048,10075}, {10783,12249}, {10792,12200}, {11370,12260}, {11388,12139}, {11497,12333}, {11824,12120}, {11901,12789}
X(12801) = reflection of X(12802) in X(7160)
X(12801) = X(7160)-of-inner-Grebe-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12802) lies on these lines: {6,7160}, {1270,9874}, {5588,9898}, {5594,12411}, {5604,8000}, {5688,12777}, {6201,12599}, {8199,12464}, {8206,12465}, {9995,12500}, {10041,10059}, {10049,10075}, {10784,12249}, {10793,12200}, {11371,12260}, {11389,12139}, {11498,12333}, {11825,12120}, {11902,12789}
X(12802) = reflection of X(12801) in X(7160)
X(12802) = X(7160)-of-outer-Grebe-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12803) lies on these lines: {6,13}, {30,7725}, {110,6215}, {568,7720}, {1163,1986}, {1271,12383}, {1511,5591}, {2771,6263}, {2777,6267}, {2931,8903}, {3448,10783}, {3581,10814}, {5589,12407}, {5595,12412}, {5663,5871}, {5689,12778}, {5875,6277}, {6202,10113}, {6218,12236}, {8198,12466}, {8205,12467}, {9994,12501}, {10088,10923}, {10091,10925}, {10792,12201}, {11370,12261}, {11388,12140}, {11497,12334}, {11824,12121}, {11901,12790}
X(12803) = reflection of X(12804) in X(265)
X(12803) = X(265)-of-inner-Grebe-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12804) lies on these lines: {6,13}, {30,7726}, {110,6214}, {568,7721}, {1162,1986}, {1270,12383}, {1511,5590}, {2771,6262}, {2777,6266}, {2931,8904}, {3448,10784}, {3581,10815}, {5588,12407}, {5594,12412}, {5663,5870}, {5688,12778}, {5874,6276}, {6201,10113}, {6217,12236}, {8199,12466}, {8206,12467}, {9995,12501}, {10088,10924}, {10091,10926}, {10793,12201}, {11371,12261}, {11389,12140}, {11498,12334}, {11825,12121}, {11902,12790}
X(12804) = reflection of X(12803) in X(265)
X(12804) = X(265)-of-outer-Grebe-triangle
The reciprocal orthologic center of these triangles is X(4).
X(12805) lies on these lines: {6,1297}, {112,11824}, {127,6202}, {132,5591}, {1271,12384}, {2781,7732}, {2794,6319}, {2799,6227}, {2806,12753}, {3320,10927}, {5589,12408}, {5595,12413}, {5689,12784}, {5861,9530}, {7725,9517}, {8198,12478}, {8205,12479}, {9994,12503}, {10783,12253}, {10792,12207}, {11370,12265}, {11388,12145}, {11497,12340}, {11901,12796}
X(12805) = X(1297)-of-inner-Grebe-triangle
X(12805) = reflection of X(12806) in X(1297)
The reciprocal orthologic center of these triangles is X(4).
X(12806) lies on these lines: {6,1297}, {112,11825}, {127,6201}, {132,5590}, {1270,12384}, {2781,7733}, {2794,6320}, {2799,6226}, {2806,12754}, {3320,10928}, {5588,12408}, {5594,12413}, {5688,12784}, {5860,9530}, {7726,9517}, {8199,12478}, {8206,12479}, {9995,12503}, {10784,12253}, {10793,12207}, {11371,12265}, {11389,12145}, {11498,12340}, {11902,12796}
X(12806) = X(1297)-of-outer-Grebe-triangle
X(12806) = reflection of X(12805) in X(1297)
The reciprocal orthologic center of these triangles is X(79).
X(12807) lies on these lines: {6,10266}, {5589,12409}, {5595,12414}, {5689,12786}, {6202,12600}, {8198,12482}, {8205,12483}, {9994,12504}, {10783,12255}, {10792,12209}, {11370,12267}, {11388,12146}, {11497,12342}, {11901,12798}
X(12807) = reflection of X(12808) in X(10266)
X(12807) = X(10266)-of-inner-Grebe-triangle
The reciprocal orthologic center of these triangles is X(79).
X(12808) lies on these lines: {6,10266}, {5588,12409}, {5594,12414}, {5688,12786}, {6201,12600}, {8199,12482}, {8206,12483}, {9995,12504}, {10784,12255}, {10793,12209}, {11371,12267}, {11389,12146}, {11498,12342}, {11902,12798}
X(12808) = reflection of X(12807) in X(10266)
X(12808) = X(10266)-of-outer-Grebe-triangle
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25581.
X(12809) lies on the incircle and these lines: {1,12810}, {65,2089}, {177,10505}, {1122,7 371}, {6018,10508}
X(12809) = X(7371)-Ceva conjugate of X(3669)
X(12809) = X(108)-of-intouch-triangle
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25582.
X(12810) lies on these lines: {1,12809}, {3,6585}
As a point of the Euler line, X(12811) has Shinagawa coefficients (7,11).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25590.
X(12811) lies on these lines: {2,3}, {517,4540}, {3303,10592}, {3304,10593}, {3614,3746}, {4701,5844}, {5418,10147}, {5420,10148}, {5563,7173}, {5609,11801}, {6488,8253}, {6489,8252}, {11695,12046}
X(12811) = midpoint of X(i) and X(j) for these {i,j}: {3,12102}, {4,3530}, {5,3850}, {140,3861}, {381,10109}, {546,3628}, {547,3860}, {3845,10124}, {5066,11737}
X(12811) = reflection of X(i) in X(j) for these (i,j): (3856,3850), (11540,547), (11695,12046), (12108,3628)
X(12811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,5,547), (4,547,3530), (4,632,12103), (4,3859,3860), (4,5070,8703), (4,5079,632), (5,3627,3090), (5,3845,1656), (140,12101,20), (381,3627,546), (546,3627,3861), (632,3627,8703), (1656,3845,548), (3090,3091,381), (3090,3627,140), (3091,3146,3855), (3525,5076,550), (3628,12102,3), (3843,5056,549), (3850,3861,381), (3861,10109,140), (5055,5076,3525)
As a point of the Euler line, X(12812) has Shinagawa coefficients (11,7).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25590.
X(12812) lies on these lines: {2,3}, {373,5876}, {576,3630}, {3303,10593}, {3304,10592}, {3614,5563}, {3625,10175}, {3633,5886}, {3635,5901}, {3746,7173}, {4668,5844}, {4691,9956}, {5305,7603}, {5690,7988}, {5943,12046}, {6560,10148}, {6561,10147}, {10095,10170}
X(12812) = midpoint of X(i) and X(j) for these {i,j}: {5,1656}, {140,3859}, {631,3858}, {632,3091}
X(12812) = reflection of X(i) in X(j) for these (i,j): (546,3091), (632,3628), (3522,3530), (3843,3850), (5071,10109)
X(12812) = complement of X(15712)
X(12812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,3627,12108), (3,11541,550), (4,5,11737), (5,3627,5072), (5,3845,5068), (140,546,12103), (546,547,3628), (546,548,3627), (546,3091,3859), (546,3628,140), (546,12103,3853), (1656,3843,2), (3091,5076,3858), (3627,3850,546), (3627,5072,3850), (3627,12108,548), (3628,3856,10303), (3843,5072,3091), (3857,12102,546), (5070,12101,140), (10303,11541,3)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25592.
X(12813) lies on these lines: {1,10502}, {164,5708}, {177,942}, {5049, 8422}, {5439,11691}, {8083,8091} ,{9957,11191}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25592.
X(12814) lies on these lines: {1,7597}, {57,3659}, {65,2089}, {174,354}, {177,942}
X(12814) = X(11)-of-intouch triangle
See Tran Quang Hung and César Lozada, Hyacinthos 25601.
X(12815) lies on these lines: {2,7765}, {4,5206}, {6,17}, {32,5056}, {115,140}, {187,3850}, {532,8260}, {533,8259}, {547,5007}, {550,3054}, {574,3533}, {629,6674}, {630,6673}, {1504,10195}, {1505,10194}, {3090,7753}, {3523,7756}, {3525,11648}, {3628,9698}, {3851,7747}, {5059,8588}, {5067,7772}, {5070,5309}, {5461,7824}, {6292,6722}
X(12815) = midpoint of X(17) and X(18)
X(12815) = reflection of X(i) in X(j) for these (i,j): (629,6674), (630,6673)
See Tran Quang Hung and César Lozada, Hyacinthos 25606.
X(12816) = outer Hung-Lozada two-hexagons point, and X(12817) = inner Hung-Lozada two-hexagons point. See Tran Quang Hung and César Lozada, Hyacinthos 25607.
Let A' be the orthocenter of BCX(17), and define B', C' cyclically. X(12816) is the centroid of A'B'C'. (Randy Hutson, July 21, 2017)
X(12816) lies on the Kiepert hyperbola and these lines: {2,10646}, {3,10188}, {5,10187}, {6,12817}, {13,3830}, {14,3845}, {16,5066}, {17,30}, {18,381}, {62,3839}, {98,5470}, {383,7608}, {395,3860}, {531,11122}, {532,5487}, {542,11602}, {671,6778}, {1080,7607}, {2043,10195}, {2044,10194}, {3412,3627}, {5071,5237}, {5485,5863}, {8781,9116}, {10159,11303}
X(12816) = isogonal conjugate of X(10645)
See Tran Quang Hung and César Lozada, Hyacinthos 25606.
X(12816) = outer Hung-Lozada two-hexagons point, and X(12817) = inner Hung-Lozada two-hexagons point. See Tran Quang Hung and César Lozada, Hyacinthos 25607.
Let A' be the orthocenter of BCX(18), and define B', C' cyclically. X(12817) is the centroid of A'B'C'. (Randy Hutson, July 21, 2017)
X(12817) lies on the Kiepert hyperbola and these lines: {2,10645}, {3,10187}, {5,10188}, {6,12816}, {13,3845}, {14,3830}, {15,5066}, {17,381}, {18,30}, {61,3839}, {98,5469}, {383,7607}, {396,3860}, {530,11121}, {533,5488}, {542,11603}, {671,6777}, {1080,7608}, {2043,10194}, {2044,10195}, {3411,3627}, {5071,5238}, {5485,5862}, {8781,9114}, {10159,11304}
X(12817) = isogonal conjugate of X(10646)
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12818) lies on the Kiepert hyperbola and these lines: {5,6434}, {6,12819}, {372,3591}, {382,485}, {486,546}, {550,10195}, {1131,6561}, {1132,6436}, {1152,11737}, {1327,6470}, {1328,3070} et al
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12819) lies on the Kiepert hyperbola and these lines: {5,6433}, {6,12818}, {371,3590}, {382,486}, {485,546}, {550,10194}, {1131,6435}, {1132,6560}, {1151,11737}, {1327,3071}, {1328,6471}
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12820) lies on the Kiepert hyperbola and these lines: {6,12821}, {17,382}, {18,546}, {383,11669}, {550,10188} et al
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12821) is the radical center of the de Longchamps circles of the adjunct anti-altimedial triangles. (Randy Hutson, November 2, 2017)
X(12821) lies on the Kiepert hyperbola and these lines: {6,12820}, {17,546}, {18,382}, {550,10187}, {1080,11669 et al
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12822) lies on the Kiepert hyperbola and these lines: {6,12823}, {30,3373}, {381,3388} et al
See Tran Quang Hung and César Lozada, Hyacinthos 25607.
X(12823) lies on the Kiepert hyperbola and these lines: {6,12822}, {30,3388}, {381,3373} et al
Let P = p : q : r be barycentrics for a point P in the plane of a triangle ABC. Let
A' = reflection of A in P, and define B' and C' cyclically
Ab = orthogonal projection of A' on AC, and define Bc and Ca cyclically
Ac = orthogonal projection of A' on AB, and define Ba and Cb cyclically
(Na) = nine-point circle of AAbAC, and define (Nb) and (Nc) cyclically
The circles concur in the point Q given by
Q = a^2 (2 a^2 b^2 c^2 p+a^4 c^2 q+b^4 c^2 q-2 a^2 c^4 q-2 b^2 c^4 q+c^6 q+a^4 b^2 r-2 a^2 b^4 r+b^6 r-2 b^4 c^2 r+b^2 c^4 r) (b^2 c^2 p^2+a^2 c^2 p q-c^4 p q+a^2 b^2 p r-b^4 p r+a^4 q r-a^2 b^2 q r-a^2 c^2 q r) : : The point Q = HM(P) is here named the Hatzipolakis-Moses nine-point image of P. The appearance of (i,j) in the following list means that X(j) = HM(X(i)): {1,11570}, {2,12824}, {4,1986}, {5,11557}, {6,5477}, {15,6783}, {16,6782}, {20,12825}, {21,12826}, {22,12827}, {23,3580}, {25,12828}, {32,12829}, {36,1737}, {39,12830}, {55,12831}, {56,12832}, {99,12833}, {110,7471}, {186,403}, {187,230}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609 and Antreas Hatzipolakis and César Lozada, Hyacinthos 25623
X(12824) lies on these lines:
{2,2781}, {23,6593}, {25,110}, {51,542}, {52,10294}, {74,9818}, {113,403}, {125,5133}, {143,5609}, {146,974}, {265,11818}, {381,5640}, {399,12236}, {511,5642}, {541,9730}, {568,5655}, {1495,11649}, {1511,2070}, {1539,11561}, {1550,11751}, {1992,2854}, {1995,9970}, {3448,7394}, {3796,10117}, {3917,5972}, {5095,8681}, {5422,5622}, {5621,10601}, {5643,12006}, {9517,9979}, {9729,10990}
X(12824) = midpoint of X(i) and X(j) for these {i,j}: {110,3060}, {568,5655}, {5890,10706}
X(12824) = reflection of X(i) in X(j) for these (i,j): (125,5943), (3060,1112), (3917,5972), (9140,12099)
X(12824) = isoconjugate of X(2157) and X(2986)
X(12824) = barycentric product X(i)*X(j) for these {i,j}: {23, 3580}, {316, 3003}
X(12824) = barycentric quotient X(i)/X(j) for these (i,j): (23, 2986), (3003, 67), (8744, 1300), (10317, 5504)
X(12824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (113,1986,12825), (113,11557,1986), (113,12828,12827), (5640,9140,12099), (12827,12828,3580)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12825) is the radical center of the polar circles of the adjunct anti-altimedial triangles. (Randy Hutson, November 2, 2017)
X(12825) lies on these lines: {2,974}, {3,74}, {22,9934}, {69, 146}, {113,403}, {125,5907} et al
X(12825) = {X(113),X(1986)}-harmonic conjugate of X(12824)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12826) lies on these lines: {21,2778}, {28,110}, {113,403} et all
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12827) lies on these lines: {2,98}, {5,12099}, {113,403} et al
X(12827) = {X(113),X(12828)}-harmonic conjugate of X(12824)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12828) lies on these lines: {4,541}, {25,542}, {51,125}, {107,11005}, {110,6353}, {112,6792} ,{113,403} et al
X(12828) = {X(12824),X(12827)}-harmonic conjugate of X(113)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12829) lies on these lines: {6,98}, {32,2782}, {39,12042}, {99,3053}, {114,230}, {115,546} et al
X(12829) = {X(114),X(5477)}-harmonic conjugate of X(12830)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12830) lies on these lines: {6,147}, {30,1569}, {98,3815}, {99,7762}, {114,230}, {115,3850} et al
X(12830) = {X(114),X(5477)}-harmonic conjugate of X(12829)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12831) lies on these lines: {11,118}, {12,5884}, {57,5660}, {63,3035}, {80,11529}, {100,3474}, {119,912} et al
X(12831) = {X(119),X(11570)}-harmonic conjugate of X(12832)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609.
X(12832) lies on these lines: {1,6713}, {10,5083}, {11,65}, {12,5883}, {46,5840}, {56,952}, {57 ,80}, {78,3035}, {100,1788}, {104 ,1470}, {109,6788}, {119,912} et al
X(12832) = {X(119),X(11570)}-harmonic conjugate of X(12831)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 25609. See also Antreas Hatzipolakis and César Lozada, Hyacinthos 25623.
X(12833) lies on these lines: {4,69}, {99,512}, {112,249}, {526,9182}, {924,4590}, {2715,4611}, {2855,9160}, {9181,10411}
X(12833) = reflection of X(99) in its Simson line (line X(114)X(325))
See Antreas Hatzipolakis and César Lozada, Hyacinthos 25612.
X(12834) lies on these lines: {2,576}, {6,11451}, {22,10541}, {25,5012}, {51,5092}, {110,5943}, {140,1173}, {182,5645}, {184,10545}, {186,5462}, {323,6688}, {373,1994}, {589,8956}, {597,11416}, {694,3108}, {1350,3060}, {1597,10574}, {2979,5644}, {3567,7514}, {3580,11548}, {5020,11422}, {5133,9140}, {5899,10095}, {9781,12083}, {9815,20009}, {10546,11402}
X(12834) = {X(5422), X(5640)}-harmonic conjugate of X(5012)
CENTERS ASSOCIATED WITH THE ELLIPSE IE59: X(12835)-X(12841)
This preamble and centers X(12835)-X(12841) were contributed by Peter Moses, March 29, 2017.
Let IE59 denote the inellipse with perspector X(59). The center of IE59 is X(13006), and IE59 passes through X(i) for these i:
55, 56, 181, 202, 203, 215, 1124, 1335, 1362, 1397, 1672, 1673, 1682, 2007, 2008, 3235, 3236, 3237, 3238, 6056, 7005, 7006, 7066, 10799, 12835, 12836, 12837, 12838, 12839, 12840, 12841
This ellipse IE59 is the locus of the centers of similtude (insimilicenter and exsimilicenter) of the incircle with Tucker circles. Also, IE59 intersects the incircle in X(1362) and three other points, so that the corresponding four Tucker circles are tangent to the incircle. The Tucker circle through X(1362) has the following parameter:
arccos[(t2 - s2)/(t2 + s2)], where t = r + 4R.
The centers of the other three Tucker circles are the extraversions of X(970), and they lie on the Brocard axis. Not only are these circle internally tangent to the incircle, but they are also externally tangent to the two corresponding excircles. In this section, the names for centers X(12835) to X(12841), the notation "Tucker (X,p)-circle" represents the Tucker circle with center X and parameter p.
Let f(a,b,c,x,y,z) = b4c4(a - b - c)2(b - c)4x2 - 2a4b2c2(a - b)2 (a - b + c)(c - a)2(a + b - c)yz. The ellipse IE59 is given by the barycentric equation f(a,b,c,x,y,z) + f(b,c,a,y,z,x) + f(c,a,b,z,x,y) = 0.
Possibly the earliest mention of IE59 occurs in TCCT, page 238, in a list of inscribed ellipses; in that list, this ellipse is denoted by W(X11).
The insimilicenter of the incircle and Tucker (X(3398),2ω) circle is X(10799).
X(12835) lies the inellipse IE(59) on these lines: {1, 3398}, {3, 10801}, {4, 10798}, {11, 98}, {12, 83}, {32, 56}, {34, 11380}, {35, 12054}, {36, 2080}, {55, 182}, {57, 10789}, {65, 12194}, {109, 727}, {181, 4279}, {388, 7787}, {499, 10104}, {999, 11842}, {1078, 5433}, {1319, 11364}, {1342, 3237}, {1343, 3238}, {1357, 1412}, {1428, 1691}, {1469, 5332}, {1478, 10796}, {1687, 2007}, {1688, 2008}, {2099, 10800}, {2276, 5038}, {2477, 3203}, {3023, 12176}, {3024, 12192}, {3027, 4027}, {3057, 12197}, {3085, 10359}, {3271, 8852}, {4293, 10788}, {5171, 5204}, {5182, 12350}, {5252, 10791}, {5434, 12150}, {6020, 12207}, {6285, 12202}, {7288, 7793}, {7354, 12110}, {10345, 10873}, {10358, 10895}, {10803, 11490}, {10944, 12195}
X(12835) = isoconjugate of X(j) and X(j) for these (i,j): {291,4518}, {334,7077}, {335,4876}
X(12835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,3398,10799), (388,7787,10797)
X(12835) = barycentric product X(i) X(j) for these {i,j}: {56,4366}, {57,8300}, {109,4375}, {238,1429}, {239,1428}, {593,3027}, {1412,4368}, {1447,1914}, {2210,10030}
X(12835) = barycentric quotient X(i)/X(j) for these (i,j): (1428,335), (1429,334), (1914,4518), (2210,4876), (4366,3596), (6652,4087), (8300,312)
X(12836) lies the inellipse IE(59) on these lines: {1, 3095}, {3, 10801}, {5, 10063}, {6,10799}, {11, 76}, {12, 262}, {35, 11171}, {36, 9821}, {39, 55}, {56, 511}, {172, 8540}, {194, 497}, {202, 3105}, {203, 3104}, {215, 3202}, {330, 1916}, {384, 10798}, {496, 10079}, {498, 11272}, {538, 11238}, {726, 12053}, {730, 1837}, {982, 3865}, {1124, 3103}, {1335, 3102}, {1362, 10571}, {1479, 2782}, {1670, 1673}, {1671, 1672}, {1689, 3235}, {1690, 3236}, {1697, 3097}, {2053, 3271}, {2275, 3056}, {3058, 7757}, {3086, 12251}, {3106, 7006}, {3107, 7005}, {4294, 7709}, {5188, 5204}, {5432, 7786}, {5969, 12351}, {6194, 7288}, {6248, 10896}, {6272, 10926}, {6273, 10925}, {6284, 11257}, {7697, 7741}, {7976, 10950}, {9581, 9902}, {9917, 10832}, {9983, 10874}, {11152, 12354}, {11376, 12263}, {11393, 12143}, {11502, 12338}
X(12836) = reflection of X(10079) in X(496)
X(12836) = barycentric product X(i) X(j) for these {i,j}: {982,3061}, {1252,3020}, {2275,3705}, {3056,3662}, {3721,3794}
X(12836) = barycentric quotient X(i)/X(j) for these (i,j): (3061,7033), (7032,7132)
X(12836) = orthologic center of these triangles: 2nd Johnson-Yff to 1st Neuberg
X(12836) = X(76)-of-2nd-Johnson-Yff-triangle
X(12836) = {X(1),X(3095)}-harmonic conjugate of X(12837)
X(12837) lies the inellipse IE(59) on these lines: {1,3095}, {3,10799}, {5,10079}, {6,12835}, {11,262}, {12,76}, {35,9821}, {36,11171}, {39,56}, {55,511}, {57,3097}, {65,12782}, {181,1403}, {192,1916}, {194,388}, {202,3106}, {203,3107}, {226,726}, {371,12839}, {372,12838}, {384,10797}, {495,10063}, {499,11272}, {538,11237}, {730,5252}, {732,12588}, {1124,3102}, {1335,3103}, {1397,5145}, {1469,2276}, {1478,2782}, {1670,1672}, {1671,1673}, {1689,3236}, {1690,3235}, {2175,8852}, {2477,3202}, {3085,12251}, {3104,7005}, {3105,7006}, {3790,7179}, {3864,7146}, {4293,7709}, {5188,5217}, {5218,6194}, {5433,7786}, {5434,7757}, {5969,12350}, {6248,10895}, {6272,10924}, {6273,10923}, {7354,11257}, {7697,7951}, {7976,10944}, {9578,9902}, {9917,10831}, {9983,10873}, {11375,12263}, {11392,12143}, {11501,12338}, {11869,12474}, {11870,12475}, {11905,12794}, {11930,12992}, {11931,12993}
X(12837) = reflection of X(10063) in X(495)
X(12837) = barycentric product X(i) X(j) for these {i,j}: {65,4469}, {226,4476}, {593,7142}, {984,7146}, {1469,3661}, {2276,7179}
X(12837) = barycentric quotient X(i)/X(j) for these (i,j): (869,2344), (4469,314), (4476,333),. (7146,870)
X(12837) = orthologic center of these triangles: 1st Johnson-Yff to 1st Neuberg
X(12837) = X(76)-of-1st-Johnson-Yff-triangle
X(12837) = {X(1),X(3095)}-harmonic conjugate of X(12836)
X(12838) lies the inellipse IE(59) on these lines: {1, 1691}, {32, 1124}, {182, 1335}, {1342, 2008}, {1343, 2007}, {1687, 3237}, {1688, 3238}, {3299, 12212}, {3301, 5038}
X(12838) = {X(1),X(1691)}-harmonic conjugate of X(12839)
X(12839) lies the inellipse IE(59) on these lines: {1, 1691}, {32, 1335}, {182, 1124}, {1342, 2007}, {1343, 2008}, {1687, 3238}, {1688, 3237}, {3299, 5038}, {3301, 12212}
X(12839) = {X(1),X(1691)}-harmonic conjugate of X(12838)
X(12840) lies the inellipse IE(59) on these lines: {1, 3094}, {39, 1124}, {55, 3102}, {56, 3103}, {371, 10799}, {511, 1335}, {1670, 3236}, {1671, 3235}, {1672, 1690}, {1673, 1689}
X(12840) = {X(1),X(3094)}-harmonic conjugate of X(12841)
X(12841) lies the inellipse IE(59) on these lines: {1, 3094}, {39, 1335}, {55, 3103}, {56, 3102}, {372, 10799}, {511, 1124}, {1670, 3235}, {1671, 3236}, {1672, 1689}, {1673, 1690}
X(12841) = {X(1),X(3094)}-harmonic conjugate of X(12840)
Orthologic centers: X(12842)-X(13005)
Centers X(12842)-X(13005) were contributed by César Eliud Lozada, April 1, 2017.
The reciprocal orthologic center of these triangles is X(3555).
X(12842) lies on these lines: {1,5920}, {3,12658}, {20,9804}, {40,6764}, {78,12533}, {84,6361}, {144,962}, {517,12654}, {1490,12692}, {3333,12855}, {3576,12521}, {5587,12620}, {5732,6762}, {5777,8158}, {7675,12846}, {7966,12245}, {8227,12612}, {8273,12333}, {8726,12439}, {9953,10864}, {10884,12537}
X(12842) = midpoint of X(i) and X(j) for these {i,j}: {1,8001}, {20,9804}
X(12842) = reflection of X(i) in X(j) for these (i,j): (40,12516), (12658,3)
The reciprocal orthologic center of these triangles is X(3555).
X(12843) lies on these lines: {1,12553}, {3,12659}, {20,12542}, {40,12517}, {78,12534}, {517,12655}, {962,4511}, {1490,12693}, {3576,12522}, {5587,12621}, {7675,12847}, {8227,12613}, {8726,12442}, {10864,12449}, {10884,12538}
X(12843) = midpoint of X(20) and X(12542)
X(12843) = reflection of X(i) in X(j) for these (i,j): (40,12517), (12659,3)
The reciprocal orthologic center of these triangles is X(1).
X(12844) lies on these lines: {1,167}, {3,164}, {20,9807}, {40,12518}, {78,11691}, {188,1490}, {517,12656}, {1482,11528}, {3333,5571}, {3576,12523}, {5587,12622}, {5732,9836}, {6765,9837}, {7587,11032}, {7588,8084}, {7670,7675}, {8075,8094}, {8076,8093}, {8227,12614}, {8726,12443}, {10864,12450}, {10884,12539}
X(12844) = midpoint of X(i) and X(j) for these {i,j}: {1,167}, {20,9807}
X(12844) = reflection of X(i) in X(j) for these (i,j): (40,12518), (164,3), (11528,1482)
X(12844) = orthologic center of these triangles: hexyl to 2nd midarc
X(12844) = {X(8081), X(8082)}-harmonic conjugate of X(1)
X(12844) = X(1)-of-hexyl-triangle
X(12844) = X(8)-of-2nd-circumperp-triangle
X(12844) = X(355)-of-excentral-triangle
X(12844) = X(944)-of-1st-circumperp-triangle
X(12844) = excentral-to-hexyl similarity image of X(164)
The reciprocal orthologic center of these triangles is X(21).
X(12845) lies on these lines: {1,5180}, {3,12660}, {20,12543}, {40,12519}, {78,12535}, {84,6597}, {411,1768}, {517,12657}, {1490,12695}, {3576,12524}, {5587,12623}, {6599,7491}, {7675,12850}, {8227,12615}, {8726,12444}, {10864,12451}, {10884,12540}
X(12845) = midpoint of X(20) and X(12543)
X(12845) = reflection of X(i) in X(j) for these (i,j): (40,12519), (12660,3)
The reciprocal orthologic center of these triangles is X(3555).
X(12846) lies on these lines: {7,3555}, {9,12533}, {1445,12658}, {2346,7160}, {4326,8001}, {5920,8236}, {7675,12842}, {7676,12516}, {7677,12521}, {7678,12612}, {7679,12620}, {8232,12692}, {8732,12439}, {9953,10865}, {10889,12552}, {11025,12855}, {11038,12853}, {11526,12654}
X(12846) = reflection of X(i) in X(j) for these (i,j): (7,12854), (12533,9)
X(12847) lies on these lines: {7,12538}, {9,12534}, {1445,12659}, {7675,12843}, {7676,12517}, {7677,12522}, {7678,12613}, {7679,12621}, {8232,12693}, {8732,12442}, {10865,12449}, {10889,12553}, {11526,12655}
X(12847) = reflection of X(12534) in X(9)
The reciprocal orthologic center of these triangles is X(1).
X(12848) lies on the cubic K295 and these lines: {1,5766}, {2,7}, {4,653}, {6,347}, {20,10394}, {44,948}, {56,6068}, {65,452}, {72,3600}, {145,4552}, {190,6604}, {218,279}, {241,4644}, {348,3758}, {388,5220}, {390,517}, {391,1441}, {405,8543}, {516,2093}, {518,3476}, {664,1992}, {954,999}, {971,2096}, {997,4321}, {1020,4253}, {1210,5735}, {1471,4310}, {1490,8544}, {1728,4295}, {1736,3332}, {1737,4312}, {1743,3668}, {1788,5177}, {1864,3474}, {2095,5762}, {2097,5845}, {2182,10402}, {2801,4293}, {3339,12572}, {3421,5686}, {3487,5265}, {3522,10393}, {3672,7961}, {3820,7679}, {3832,10395}, {4294,10399}, {4308,11523}, {4323,5436}, {4326,7994}, {4419,5228}, {4641,7365}, {4848,5175}, {5173,10177}, {5218,8255}, {5223,12573}, {5704,5715}, {5740,5798}, {5779,6826}, {5784,6904}, {5805,6844}, {5812,11662}, {5817,6843}, {5843,6911}, {5924,7682}, {6244,7676}, {6282,7675}, {7678,7956}, {7962,8236}, {8101,8387}, {8102,8388}, {9954,10865}, {10889,12555}
X(12848) = midpoint of X(144) and X(9965)
X(12848) = reflection of X(i) in X(j) for these (i,j): (7,57), (329,9), (5809,10398)
X(12848) = X(25)-of-Honsberger-triangle
X(12848) = excentral-to-Honsberger similarity image of X(57)
X(12848) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7,9,8232), (7,1445,8732), (7,6172,8545), (390,7672,12849), (5728,5759,390)
The reciprocal orthologic center of these triangles is X(79)
X(12849) lies on these lines: {2,3467}, {3,12255}, {4,12146}, {5,13126}, {7,6597}, {8,12535}, {10,12409}, {20,5694}, {22,12414}, {100,12342}, {145,13100}, {149,6595}, {153,5690}, {388,12947}, {497,12957}, {1270,12808}, {1271,12807}, {2475,12745}, {2896,12504}, {3085,13128}, {3086,13129}, {3091,12600}, {3434,12927}, {3436,12937}, {3616,12267}, {3648,3988}, {3878,6224}, {4240,12798}, {4309,12877}, {5601,12482}, {5602,12483}, {6462,13000}, {6463,13001}, {7787,12209}, {10528,13130}, {10529,13131}
X(12849) = reflection of X(i) in X(j) for these (i,j): (4,12919), (8,12786), (20,12556), (145,13100), (149,6595), (4240,12798), (10266,13089), (12255,3), (12409,10), (12535,12682), (12543,6597), (13126,5)
X(12849) = anticomplement of X(10266)
X(12849) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10266,13089,2), (12957,13080,497)
The reciprocal orthologic center of these triangles is X(21).
X(12850) lies on these lines: {7,6597}, {9,12535}, {1445,12660}, {2346,10266}, {3889,12701}, {7675,12845}, {7676,12519}, {7677,12524}, {7678,12615}, {7679,12623}, {8232,12695}, {8732,12444}, {10865,12451}, {10889,12557}, {11526,12657}
X(12850) = reflection of X(12535) in X(9)
The reciprocal orthologic center of these triangles is X(3555).
X(12851) lies on these lines: {363,12658}, {5920,8390}, {5934,12692}, {8001,8140}, {8107,12516}, {8109,12521}, {8377,12612}, {8380,12620}, {9783,9804}, {9953,11856}, {11527,12654}, {11685,12533}, {11854,12439}, {11886,12537}, {11892,12552}
X(12851) = reflection of X(12852) in X(8001)
The reciprocal orthologic center of these triangles is X(3555).
X(12852) lies on these lines: {168,12658}, {5920,8392}, {5935,12692}, {7160,7707}, {8001,8140}, {8108,12516}, {8110,12521}, {8378,12612}, {8381,12620}, {9787,9804}, {9953,11857}, {11528,12654}, {11686,12533}, {11855,12439}, {11887,12537}, {11893,12552}
X(12852) = reflection of X(12851) in X(8001)
The reciprocal orthologic center of these triangles is X(3555).
X(12853) lies on these lines: {1,5920}, {495,12620}, {496,12612}, {942,12439}, {999,12521}, {3295,12516}, {3333,12658}, {3487,12692}, {3616,12533}, {4295,12680}, {4326,6766}, {5045,12855}, {5542,9953}, {6764,12777}, {8351,12871}, {9797,9874}, {9804,11037}, {11036,12537}, {11038,12846}, {11042,12865}, {11043,12869}, {11529,12654}
X(12853) = midpoint of X(1) and X(12854)
X(12853) = reflection of X(12855) in X(5045)
X(12853) = {X(1), X(8001)}-harmonic conjugate of X(7160)
The reciprocal orthologic center of these triangles is X(3555).
X(12854) lies on these lines: {1,5920}, {2,12533}, {11,12612}, {12,12620}, {55,12516}, {56,12521}, {57,12439}, {72,11526}, {174,12871}, {226,12692}, {354,12855}, {1284,12869}, {2089,12870}, {3340,12654}, {3555,5082}, {5173,12777}, {8243,12865}, {8581,9953}, {12670,12864}, {12731,12859}
X(12854) = midpoint of X(i) and X(j) for these {i,j}: {7,12846}, {9804,12537}
X(12854) = reflection of X(i) in X(j) for these (i,j): (1,12853), (5920,1), (12658,12439), (12670,12864)
X(12854) = complement of X(12533)
The reciprocal orthologic center of these triangles is X(3555).
X(12855) lies on these lines: {1,12521}, {7,40}, {10,5572}, {57,12516}, {65,5920}, {142,3913}, {226,9589}, {354,12854}, {495,12599}, {942,11362}, {946,3295}, {1056,12120}, {1210,12620}, {3085,7308}, {3303,12859}, {3333,12842}, {3339,9898}, {3873,12533}, {3922,12736}, {4866,10398}, {5045,12853}, {5703,9624}, {5728,12692}, {6767,12856}, {8001,10980}, {8083,12873}, {9804,10580}, {9874,11024}, {9953,11019}, {10056,10075}, {10122,12670}, {11018,12439}, {11020,12537}, {11021,12552}, {11025,12846}, {11030,12865}, {11031,12869}, {11032,12870}, {11033,12871}
X(12855) = midpoint of X(i) and X(j) for these {i,j}: {65,5920}, {12658,12777}
X(12855) = reflection of X(12853) in X(5045)
The reciprocal orthologic center of these triangles is X(40).
X(12856) lies on these lines: {1,12859}, {2,12249}, {3,12411}, {4,9874}, {5,7160}, {11,10075}, {12,10059}, {30,12120}, {355,12731}, {381,12599}, {517,12777}, {952,5665}, {1479,12863}, {3652,12516}, {5587,9898}, {5779,12699}, {5805,6601}, {5886,12260}, {6214,12802}, {6215,12801}, {6265,12521}, {6767,12855}, {6864,9957}, {8200,12464}, {8207,12465}, {8220,12861}, {8221,12862}, {9996,12500}, {10796,12200}, {10942,12874}, {10943,12875}, {11499,12333}
X(12856) = midpoint of X(i) and X(j) for these {i,j}: {4,9874}, {12857,12858}
X(12856) = reflection of X(i) in X(j) for these (i,j): (3,12864), (7160,5), (12872,12599)
X(12856) = complement of X(12249)
X(12856) = X(7160)-of-Johnson-triangle
X(12856) = {X(12859),X(12860)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(40).
X(12857) lies on these lines: {11,7160}, {12,12874}, {355,12731}, {1376,12333}, {8000,10944}, {9898,10826}, {10059,10523}, {10075,10948}, {10785,12249}, {10794,12200}, {10829,12411}, {10871,12500}, {10893,12599}, {10914,12777}, {10919,12801}, {10920,12802}, {10945,12861}, {10946,12862}, {10947,12863}, {10949,12875}, {11373,12260}, {11390,12139}, {11826,12120}, {11865,12464}, {11866,12465}, {11903,12789}, {11928,12872}
X(12857) = reflection of X(i) in X(j) for these (i,j): (12333,12864), (12858,12856)
X(12857) = X(7160)-of-inner-Johnson-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12858) lies on these lines: {4,5173}, {11,12875}, {12,7160}, {72,12777}, {355,12731}, {946,3295}, {958,12864}, {2886,5791}, {3436,9874}, {5220,5812}, {5572,5805}, {8000,10950}, {9898,10827}, {10059,10954}, {10075,10523}, {10786,12249}, {10795,12200}, {10830,12411}, {10872,12500}, {10894,12599}, {10921,12801}, {10922,12802}, {10951,12861}, {10952,12862}, {10953,12863}, {10955,12874}, {11391,12139}, {11827,12120}, {11867,12464}, {11868,12465}, {11904,12789}, {11929,12872}
X(12858) = reflection of X(12857) in X(12856)
X(12858) = X(7160)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12859) lies on these lines: {1,12856}, {4,12863}, {5,10075}, {12,7160}, {56,12864}, {65,12777}, {354,11023}, {388,9874}, {495,10059}, {3085,12249}, {3303,12855}, {4863,5173}, {7354,12120}, {8000,10944}, {9654,12872}, {10797,12200}, {10831,12411}, {10873,12500}, {10895,12599}, {10923,12801}, {10924,12802}, {10956,12874}, {10957,12875}, {11375,12260}, {11392,12139}, {11501,12333}, {11905,12789}, {11930,12861}, {11931,12862}, {12731,12854}
X(12859) = reflection of X(10059) in X(495)
X(12859) = X(7160)-of-1st-Johnson-Yff-triangle
X(12859) = {X(1),X(12856)}-harmonic conjugate of X(12860)
The reciprocal orthologic center of these triangles is X(40).
X(12860) lies on these lines: {1,12856}, {5,10059}, {11,7160}, {55,12864}, {480,12053}, {496,10075}, {497,9874}, {3057,12777}, {3086,12249}, {3601,6154}, {5920,12731}, {6284,12120}, {8000,10950}, {9581,9898}, {9669,12872}, {10798,12200}, {10832,12411}, {10874,12500}, {10896,12599}, {10925,12801}, {10926,12802}, {10958,12874}, {10959,12875}, {11376,12260}, {11393,12139}, {11502,12333}, {11871,12464}, {11872,12465}, {11906,12789}, {11932,12861}, {11933,12862}
X(12860) = reflection of X(10075) in X(496)
X(12860) = X(7160)-of-2nd-Johnson-Yff-triangle
X(12860) = {X(1),X(12856)}-harmonic conjugate of X(12859)
The reciprocal orthologic center of these triangles is X(40).
X(12861) lies on these lines: {493,7160}, {6461,12862}, {6462,9874}, {8000,8210}, {8188,9898}, {8194,12411}, {8201,12464}, {8208,12465}, {8212,12599}, {8214,12777}, {8216,12801}, {8218,12802}, {8220,12856}, {8222,12864}, {10059,11951}, {10875,12500}, {11377,12260}, {11394,12139}, {11503,12333}, {11828,12120}, {11840,12200}, {11846,12249}, {11930,12859}, {11932,12860}, {11947,12863}, {11949,12872}, {11955,12874}, {11957,12875}
X(12861) = X(7160)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12862) lies on these lines: {494,7160}, {6461,12861}, {6463,9874}, {8000,8211}, {8189,9898}, {8195,12411}, {8202,12464}, {8209,12465}, {8213,12599}, {8215,12777}, {8217,12801}, {8219,12802}, {8221,12856}, {8223,12864}, {10059,11952}, {10075,11954}, {10876,12500}, {11378,12260}, {11395,12139}, {11504,12333}, {11829,12120}, {11841,12200}, {11847,12249}, {11931,12859}, {11933,12860}, {11948,12863}, {11950,12872}, {11956,12874}, {11958,12875}
X(12862) = X(7160)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12863) lies on these lines: {3,10075}, {4,12859}, {11,12864}, {12,12599}, {33,12139}, {55,84}, {56,12120}, {497,9874}, {1479,12856}, {1697,5223}, {1837,12777}, {2098,8000}, {2646,12260}, {3057,3488}, {3295,10059}, {3601,9850}, {4294,12249}, {5920,10543}, {10799,12200}, {10833,12411}, {10877,12500}, {10927,12801}, {10928,12802}, {10947,12857}, {10953,12858}, {10965,12874}, {10966,12875}, {11873,12464}, {11874,12465}, {11909,12789}, {11947,12861}, {11948,12862}
X(12863) = X(7160)-of-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(40).
X(12864) lies on these lines: {1,12521}, {2,7160}, {3,12411}, {4,12120}, {5,12599}, {8,8000}, {9,946}, {11,12863}, {55,12860}, {56,12859}, {83,12200}, {142,5045}, {427,12139}, {442,3555}, {498,10059}, {499,10075}, {631,12249}, {958,12858}, {1125,6600}, {1145,4002}, {1376,12333}, {1650,12789}, {1656,12872}, {1698,9898}, {2886,6260}, {3090,12612}, {3096,12500}, {3333,9776}, {3889,12537}, {5552,12874}, {5590,12802}, {5591,12801}, {5599,12464}, {5600,12465}, {5795,6849}, {6864,9623}, {8222,12861}, {8223,12862}, {9709,12631}, {10527,12875}, {12670,12854}
X(12864) = midpoint of X(i) and X(j) for these {i,j}: {1,12777}, {3,12856}, {4,12120}, {8,8000}, {1650,12789}, {3555,12692}, {7160,9874}, {12333,12857}, {12521,12731}, {12670,12854}
X(12864) = reflection of X(i) in X(j) for these (i,j): (12260,1125), (12439,5045), (12599,5)
X(12864) = complement of X(7160)
X(12864) = {X(2), X(9874)}-harmonic conjugate of X(7160)
The reciprocal orthologic center of these triangles is X(3555).
X(12865) lies on these lines: {5920,8239}, {8001,8244}, {8224,12516}, {8225,12521}, {8228,12612}, {8230,12620}, {8231,12658}, {8233,12692}, {8234,12842}, {8237,12846}, {8243,12854}, {8246,12869}, {9789,9804}, {9953,10867}, {10858,12439}, {10885,12537}, {10891,12552}, {11030,12855}, {11042,12853}, {11532,12654}, {11687,12533}, {11996,12873}
The reciprocal orthologic center of these triangles is X(12867).
X(12866) lies on these lines: {9,10266}, {20,5538}, {65,2475}, {6597,12444}, {11024,12543}
X(12866) = reflection of X(i) in X(j) for these (i,j): (6597,12444), (12682,12660), (12695,12639)
The reciprocal orthologic center of these triangles is X(12866).
X(12867) lies on the Feuerbach hyperbola and these lines: {7,442}, {30,10429}, {84,3651}, {191,3062}, {210,943}, {758,5665}, {3647,7285}, {4900,9898}, {5556,11684}
The reciprocal orthologic center of these triangles is X(12632).
X(12868) lies on the Feuerbach hyperbola and these lines: {7,12732}, {90,12756}, {100,5558}, {952,10429}, {1000,4423}, {2802,5665}, {6601,8168}
X(12868) = reflection of X(100) in X(12631)
The reciprocal orthologic center of these triangles is X(3555).
X(12869) lies on these lines: {21,3870}, {846,12658}, {1284,12854}, {4199,12692}, {4220,12516}, {5051,12620}, {5920,8240}, {8001,8245}, {8229,12612}, {8235,12842}, {8238,12846}, {8246,12865}, {8249,12870}, {8425,12873}, {8731,12439}, {9953,10868}, {10892,12552}, {11031,12855}, {11043,12853}, {11533,12654}, {11688,12533}
X(12869) = 2nd-Sharygin-to-1st-Sharygin similarity image of X(13286)
X(12869) = excentral-to-1st-Sharygin similarity image of X(12658)
X(12869) = hexyl-to-1st-Sharygin similarity image of X(12842)
X(12869) = Hutson-intouch-to-1st-Sharygin similarity image of X(5920)
The reciprocal orthologic center of these triangles is X(3555).
X(12870) lies on these lines: {1,12871}, {2089,12854}, {5920,8241}, {8001,8089}, {8075,12516}, {8077,12521}, {8078,12658}, {8079,12692}, {8081,12842}, {8085,12612}, {8087,12620}, {8247,12865}, {8249,12869}, {8387,12846}, {8733,12439}, {9793,9804}, {11032,12855}, {11690,12533}, {11888,12537}, {11894,12552}
X(12870) = reflection of X(12871) in X(1)
The reciprocal orthologic center of these triangles is X(3555).
X(12871) lies on these lines: {1,12870}, {174,12854}, {258,12658}, {7588,12521}, {8125,12533}, {8351,12853}, {8734,12439}, {9953,11859}, {11033,12855}, {11895,12552}, {11899,12654}
X(12871) = reflection of X(12870) in X(1)
The reciprocal orthologic center of these triangles is X(40).
X(12872) lies on these lines: {3,7091}, {5,9874}, {30,12249}, {381,12599}, {517,9898}, {960,1482}, {999,10075}, {1598,12139}, {1656,12864}, {3295,10059}, {5790,12777}, {7517,12411}, {8000,10247}, {9301,12500}, {9654,12859}, {9669,12860}, {10246,12260}, {10679,12631}, {11842,12200}, {11849,12333}, {11875,12464}, {11876,12465}, {11911,12789}, {11916,12801}, {11917,12802}, {11928,12857}, {11929,12858}, {11949,12861}, {11950,12862}, {12000,12874}, {12001,12875}
X(12872) = reflection of X(i) in X(j) for these (i,j): (3,7160), (9874,5), (12856,12599)
X(12872) = X(7160)-of-X3-ABC-reflections-triangle
The reciprocal orthologic center of these triangles is X(3555).
X(12873) lies on these lines: {174,12854}, {5920,11924}, {7587,12521}, {8001,8423}, {8083,12855}, {8126,12533}, {8382,12620}, {8389,12846}, {8425,12869}, {8729,12439}, {9804,11891}, {9953,11860}, {11535,12654}, {11890,12537}, {11896,12552}, {11996,12865}
The reciprocal orthologic center of these triangles is X(40).
X(12874) lies on these lines: {1,5920}, {12,12857}, {5552,12864}, {9874,10528}, {10531,12599}, {10803,12200}, {10805,12249}, {10834,12411}, {10878,12500}, {10915,12777}, {10929,12801}, {10930,12802}, {10942,12856}, {10955,12858}, {10956,12859}, {10958,12860}, {10965,12863}, {11248,12120}, {11400,12139}, {11509,12333}, {11881,12464}, {11882,12465}, {11914,12789}, {11955,12861}, {11956,12862}, {12000,12872}
X(12874) = reflection of X(7160) in X(10059)
X(12874) = X(7160)-of-inner-Yff-tangents-triangle
X(12874) = {X(7160),X(8000)}-harmonic conjugate of X(12875)
The reciprocal orthologic center of these triangles is X(40).
X(12875) lies on these lines: {1,5920}, {2,10941}, {9,6675}, {11,12858}, {56,12687}, {57,6833}, {938,10936}, {1210,12116}, {1445,12704}, {6734,12620}, {6878,11048}, {9874,10529}, {10527,12864}, {10532,12599}, {10804,12200}, {10806,12249}, {10835,12411}, {10879,12500}, {10916,12777}, {10931,12801}, {10932,12802}, {10943,12856}, {10949,12857}, {10957,12859}, {10959,12860}, {10966,12863}, {11249,12120}, {11401,12139}, {11510,12333}, {11883,12464}, {11884,12465}, {11915,12789}, {11957,12861}, {11958,12862}, {12001,12872}
X(12875) = reflection of X(7160) in X(10075)
X(12875) = X(7160)-of-outer-Yff-tangents-triangle
X(12875) = {X(7160),X(8000)}-harmonic conjugate of X(12874)
The reciprocal orthologic center of these triangles is X(3555).
X(12876) lies on these lines: {1,12553}, {11,12621}, {12,12613}, {34,517}, {55,12522}, {56,12517}, {145,12534}, {522,10912}, {950,12693}, {1482,4292}, {1697,12659}, {3601,12442}, {4313,12538}, {7962,12655}, {8236,12847}, {8390,12878}, {8392,12883}, {9785,12542}, {10866,12449}
X(12876) = midpoint of X(145) and X(12534)
X(12876) = reflection of X(12912) in X(1)
The reciprocal orthologic center of these triangles is X(21).
X(12877) lies on these lines: {1,5180}, {8,6597}, {11,21}, {12,12615}, {35,2475}, {55,12524}, {145,12535}, {950,12695}, {1697,12660}, {3057,12682}, {3601,12444}, {3648,4018}, {4294,10043}, {4313,12540}, {5441,12758}, {6872,10051}, {7962,12657}, {8236,12850}, {8390,12882}, {8392,12887}, {9785,12543}, {10866,12451}
X(12877) = midpoint of X(145) and X(12535)
X(12877) = reflection of X(12913) in X(1)
The reciprocal orthologic center of these triangles is X(3555).
X(12878) lies on these lines: {363,12659}, {5934,12693}, {8107,12517}, {8109,12522}, {8111,12843}, {8140,12883}, {8377,12613}, {8380,12621}, {8385,12847}, {8390,12876}, {9783,12542}, {11527,12655}, {11685,12534}, {11854,12442}, {11856,12449}, {11886,12538}, {11892,12553}
The reciprocal orthologic center of these triangles is X(1).
X(12879) lies on these lines: {1,6724}, {40,164}, {167,8140}, {177,8113}, {1130,11923}, {3577,11528}, {5571,11026}, {5934,11523}, {7670,8385}, {8107,12518}, {8390,8422}, {9783,9807}, {11685,11691}, {11856,12450}, {11886,12539}, {11892,12554}
X(12879) = reflection of X(i) in X(j) for these (i,j): (164,188), (12884,167)
X(12879) = orthologic center of these triangles: inner-Hutson to 2nd midarc
X(12879) = X(1)-of-inner-Hutson-triangle
X(12879) = excentral-to-inner-Hutson similarity image of X(164)
X(12879) = {X(6732),X(8133)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(1).
X(12880) lies on these lines: {57,363}, {329,5934}, {999,8109}, {3820,8380}, {6244,8107}, {6282,8111}, {7956,8377}, {7962,8390}, {7994,8140}, {8101,8133}, {8385,12848}, {9954,11856}, {9965,11886}, {11892,12555}
X(12880) = reflection of X(12885) in X(7994)
X(12880) = X(25)-of-inner-Hutson-triangle
X(12880) = excentral-to-inner-Hutson similarity image of X(57)
The reciprocal orthologic center of these triangles is X(1)
X(12881) lies on these lines: {168,12396}, {5935,12397}, {7707,12406}, {8108,12387}, {8110,12388}, {8112,12398}, {8114,12402}, {8140,12404}, {8378,12393}, {8381,12394}, {8386,12399}, {8392,12400}, {9787,12391}, {11027,12403}, {11040,12401}, {11528,12395}, {11686,12389}, {11855,12385}, {11857,12386}, {11887,12390}, {11893,12392}, {11926,12405}
The reciprocal orthologic center of these triangles is X(21).
X(12882) lies on these lines: {363,12660}, {5934,12695}, {8107,12519}, {8109,12524}, {8111,12845}, {8140,12887}, {8377,12615}, {8380,12623}, {8385,12850}, {8390,12877}, {9783,12543}, {11527,12657}, {11685,12535}, {11854,12444}, {11856,12451}, {11886,12540}, {11892,12557}
The reciprocal orthologic center of these triangles is X(3555).
X(12883) lies on these lines: {5935,12693}, {8108,12517}, {8110,12522}, {8112,12843}, {8140,12878}, {8378,12613}, {8381,12621}, {8386,12847}, {8392,12876}, {11528,12655}, {11686,12534}, {11855,12442}, {11857,12449}, {11887,12538}, {11893,12553}
The reciprocal orthologic center of these triangles is X(1).
X(12884) lies on these lines: {1,8135}, {9,164}, {177,8114}, {5571,11027}, {7670,8386}, {7982,9837}, {8108,12518}, {8110,12523}, {8140,10233}, {8378,12614}, {8381,12622}, {8392,8422}, {9787,9807}, {11686,11691}, {11855,12443}, {11857,12450}, {11887,12539}, {11893,12554}
X(12884) = reflection of X(i) in X(j) for these (i,j): (11528,9837), (12879,167)
X(12884) = orthologic center of these triangles: outer-Hutson to 2nd midarc
X(12884) = X(1)-of-outer-Hutson-triangle
X(12884) = excentral-to-outer-Hutson similarity image of X(164)
X(12884) = {X(8135),X(8138)}-harmonic conjugate of X(1)
The reciprocal orthologic center of these triangles is X(1).
X(12885) lies on these lines: {329,5935}, {999,8110}, {3820,8381}, {6244,8108}, {6282,8112}, {7956,8378}, {7994,8140}, {8101,8135}, {8102,8138}, {8386,12848}, {9954,11857}, {9965,11887}, {11893,12555}
X(12885) = reflection of X(12880) in X(7994)
X(12885) = X(25)-of-outer-Hutson-triangle
X(12885) = excentral-to-outer-Hutson similarity image of X(57)
The reciprocal orthologic center of these triangles is X(1)
X(12886) lies on these lines: {363,12396}, {5934,12397}, {8107,12387}, {8109,12388}, {8111,12398}, {8113,12402}, {8140,12404}, {8377,12393}, {8380,12394}, {8385,12399}, {8390,12400}, {8391,12405}, {9783,12391}, {11026,12403}, {11039,12401}, {11527,12395}, {11685,12389}, {11854,12385}, {11856,12386}, {11886,12390}, {11892,12392}, {11923,12406}
The reciprocal orthologic center of these triangles is X(21).
X(12887) lies on these lines: {5935,12695}, {8108,12519}, {8110,12524}, {8112,12845}, {8140,12882}, {8378,12615}, {8381,12623}, {8386,12850}, {8392,12877}, {11528,12657}, {11686,12535}, {11855,12444}, {11857,12451}, {11887,12540}, {11893,12557}
The reciprocal orthologic center of these triangles is X(10112).
X(12888) lies on the intangents circle and these lines: {1,12896}, {33,113}, {34,12295}, {35,12893}, {36,12901}, {55,2931}, {56,12302}, {74,3100}, {110,6198}, {125,1062}, {146,9539}, {399,3157}, {497,12319}, {1040,6699}, {1250,10664}, {1870,10733}, {2066,12891}, {2948,9577}, {3031,9551}, {3043,9637}, {3047,9638}, {3295,12310}, {3448,9538}, {4354,10065}, {5414,12892}, {5504,10091}, {5663,6285}, {7071,12168}, {8540,12596}, {9576,9904}, {9627,12903}, {9628,12373}, {9629,12374}, {9630,12904}, {9632,10819}, {9633,10817}, {9641,10620}, {9645,10117}, {9817,12900}, {10638,10663}, {11429,12228}, {11436,12236}, {11446,12273}, {11461,12284}
X(12888) = reflection of X(i) in X(j) for these (i,j): (10118,8144), (12661,2931)
X(12888) = antipode of X(10118) in intangents circle
The reciprocal orthologic center of these triangles is X(6102).
X(12889) lies on these lines: {11,265}, {12,12905}, {30,12371}, {110,355}, {542,12586}, {1376,1511}, {2771,7984}, {3434,12383}, {3448,10785}, {5663,12114}, {10088,10944}, {10113,10893}, {10523,12903}, {10794,12201}, {10826,12407}, {10829,12412}, {10871,12501}, {10914,12778}, {10919,12803}, {10920,12804}, {10945,12894}, {10946,12895}, {10947,12896}, {10948,12904}, {10949,12906}, {11373,12261}, {11390,12140}, {11826,12121}, {11903,12790}, {11928,12902}
X(12889) = reflection of X(i) in X(j) for these (i,j): (12334,1511), (12890,110)
The reciprocal orthologic center of these triangles is X(6102).
X(12890) lies on these lines: {11,12906}, {12,265}, {30,12372}, {72,74}, {110,355}, {542,12587}, {958,1511}, {3436,12383}, {3448,10786}, {5663,11500}, {6253,7728}, {10091,10950}, {10113,10894}, {10523,12904}, {10795,12201}, {10827,12407}, {10830,12412}, {10872,12501}, {10921,12803}, {10922,12804}, {10951,12894}, {10952,12895}, {10953,12896}, {10954,12903}, {10955,12905}, {11374,12261}, {11391,12140}, {11827,12121}, {11904,12790}, {11929,12902}
X(12890) = reflection of X(12889) in X(110)
X(12890) = X(265)-of-outer-Johnson-triangle
The reciprocal orthologic center of these triangles is X(10112).
X(12891) lies on these lines: {6,1511}, {74,11417}, {110,10666}, {113,5412}, {125,10897}, {265,6413}, {372,12893}, {1151,12302}, {2066,12888}, {3068,12319}, {3311,12310}, {5410,12168}, {5415,12661}, {5663,11265}, {6699,11513}, {10961,12900}, {11447,12273}, {11462,12284}, {11473,12295}
X(12891) = {X(6),X(2931)}-harmonic conjugate of X(12892)
The reciprocal orthologic center of these triangles is X(10112).
X(12892) lies on these lines: {6,1511}, {74,11418}, {110,10665}, {113,5413}, {125,10898}, {265,6414}, {371,12893}, {1152,12302}, {3069,12319}, {3312,12310}, {5411,12168}, {5414,12888}, {5416,12661}, {5663,11266}, {6396,12901}, {6699,11514}, {10963,12900}, {11448,12273}, {11463,12284}, {11474,12295}
X(12892) = {X(6),X(2931)}-harmonic conjugate of X(12891)
The reciprocal orthologic center of these triangles is X(10112).
X(12893) lies on these lines: {3,125}, {15,10664}, {16,10663}, {23,10721}, {24,113}, {26,2777}, {35,12888}, {54,5504}, {68,5963}, {74,7488}, {110,186}, {371,12892}, {372,12891}, {378,12295}, {389,11536}, {399,12163}, {541,10117}, {549,11804}, {575,12596}, {578,12236}, {631,12319}, {1147,1511}, {1658,5663}, {2070,7728}, {2935,7387}, {3043,5889}, {3047,11464}, {3448,10298}, {3515,12168}, {3520,10733}, {3564,12584}, {5972,6644}, {6642,12900}, {6723,7514}, {7502,8717}, {7526,7687}, {7556,12244}, {8723,9517}, {8998,9682}, {9590,12368}, {9932,10114}, {10821,12235}, {10902,12661}, {11430,11800}, {11449,12273}
X(12893) = midpoint of X(i) and X(j) for these {i,j}: {3,2931}, {68,12383}, {399,12163}, {2935,7387}, {12302,12310}
X(12893) = reflection of X(i) in X(j) for these (i,j): (265,5449), (1147,1511), (5504,12038), (12596,575), (12901,3)
X(12893) = anticomplement of X(33547)
X(12893) = {X(3), X(12310)}-harmonic conjugate of X(12302)
The reciprocal orthologic center of these triangles is X(6102).
X(12894) lies on these lines: {30,12377}, {110,8220}, {265,493}, {542,12590}, {1511,8222}, {2771,12741}, {3448,11846}, {5663,9838}, {6461,12895}, {6462,12383}, {8188,12407}, {8194,12412}, {8210,12898}, {8212,10113}, {8214,12778}, {8216,12803}, {8218,12804}, {10088,11930}, {10091,11932}, {10875,12501}, {10945,12889}, {11377,12261}, {11394,12140}, {11503,12334}, {11828,12121}, {11840,12201}, {11907,12790}, {11947,12896}, {11949,12902}, {11951,12903}, {11953,12904}, {11955,12905}, {11957,12906}
X(12894) = X(265)-of-Lucas-homothetic-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12895) lies on these lines: {30,12378}, {110,8221}, {265,494}, {542,12591}, {1511,8223}, {2771,12742}, {3448,11847}, {5663,9839}, {6461,12894}, {6463,12383}, {8189,12407}, {8195,12412}, {8211,12898}, {8213,10113}, {8215,12778}, {8217,12803}, {8219,12804}, {10088,11931}, {10091,11933}, {10946,12889}, {11378,12261}, {11395,12140}, {11504,12334}, {11829,12121}, {11841,12201}, {11908,12790}, {11948,12896}, {11950,12902}, {11952,12903}, {11954,12904}, {11956,12905}, {11958,12906}
X(12895) = X(265)-of-Lucas(-1)-homothetic-triangle
The reciprocal orthologic center of these triangles is X(6102).
X(12896) lies on these lines: {1,12888}, {3,12904}, {4,10088}, {11,1511}, {12,10113}, {20,10081}, {30,3028}, {33,12140}, {35,125}, {55,265}, {56,12121}, {74,4302}, {79,6062}, {80,4092}, {110,1479}, {113,3583}, {382,12373}, {399,9668}, {497,10091}, {542,3056}, {1478,10733}, {1697,12407}, {1837,12778}, {2098,12898}, {2646,12261}, {2771,12743}, {2777,7355}, {2948,3586}, {3295,12902}, {3448,4294}, {3585,12295}, {5010,6699}, {5663,6284}, {5972,7741}, {7687,7951}, {10058,10778}, {10086,11005}, {10799,12201}, {10833,12412}, {10877,12501}, {10927,12803}, {10928,12804}, {10947,12889}, {10953,12890}, {10965,12905}, {10966,12906}, {11874,12467}, {11909,12790}, {11947,12894}, {11948,12895}
X(12896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (399,9668,12374), (497,12383,10091), (3295,12902,12903), (3448,4294,10065)
X(12896) = X(265)-of-Mandart-incircle-triangle
The reciprocal orthologic center of these triangles is X(7687).
X(12897) lies on these lines: {4,110}, {30,143}, {195,7728}, {235,12038}, {378,5449}, {382,1181}, {539,12162}, {568,10937}, {1209,7527}, {1493,2883}, {1533,10619}, {1593,9927}, {1597,12293}, {1885,12421}, {2777,6102}, {2781,12585}, {3146,11750}, {3543,12289}, {5073,11820}, {5097,8550}, {5663,10112}, {6000,10116}, {6699,11250}, {7687,10224}, {7706,10982}, {10575,12022}, {10628,12899}, {11472,12429}
X(12897) = midpoint of X(3146) and X(11750)
X(12897) = reflection of X(10116) in X(12370)
X(12897) = X(1320)-of-1st-Hyacinth-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(6102).
X(12898) lies on these lines: {1,265}, {8,1511}, {30,6742}, {56,12334}, {110,952}, {125,10246}, {145,12383}, {355,11720}, {381,11723}, {515,7728}, {517,12121}, {519,12778}, {542,3242}, {944,5663}, {1483,7979}, {2098,12896}, {2771,3057}, {2777,7973}, {3448,7967}, {3655,11709}, {5597,12467}, {5598,12466}, {5603,10113}, {5604,12804}, {5605,12803}, {5655,11699}, {5790,5972}, {8192,12412}, {8210,12894}, {8211,12895}, {9997,12501}, {10088,10944}, {10091,10950}, {10247,12902}, {10283,11801}, {10800,12201}, {11396,12140}, {11910,12790}
X(12898) = midpoint of X(145) and X(12383)
X(12898) = reflection of X(i) in X(j) for these (i,j): (8,1511), (265,1), (355,11720), (7984,1483), (12368,11699), (12407,12261)
X(12898) = X(265)-of-5th-mixtilinear-triangle
X(12898) = {X(12905),X(12906)}-harmonic conjugate of X(265)
The reciprocal orthologic center of these triangles is X(399).
X(12899) lies on these lines: {5,11536}, {195,10255}, {389,539}, {567,3519}, {1154,12370}, {1209,1493}, {1353,9977}, {2888,12161}, {6102,11562}, {10115,12236}, {10628,12897}, {11801,11803}
The reciprocal orthologic center of these triangles is X(10112).
X(12900) lies on these lines: {2,74}, {5,1511}, {10,11723}, {110,569}, {125,399}, {140,2777}, {265,5642}, {486,8998}, {542,3589}, {690,6721}, {974,5892}, {1112,1216}, {1209,2914}, {1568,3581}, {1986,5891}, {2771,6667}, {3619,10752}, {3624,12368}, {3819,11807}, {5448,11438}, {5449,12227}, {5663,9729}, {5943,12236}, {6053,10264}, {7978,9780}, {8253,8994}, {9306,12228}, {9813,12596}, {9817,12888}, {9827,11746}, {10170,11557}, {10546,12140}, {10643,10663}, {10644,10664}, {10961,12891}, {10963,12892}, {11230,11735}, {11451,12273}, {11465,12284}
X(12900) = midpoint of X(i) and X(j) for these {i,j}: {5,5972}, {10,11723}, {113,6699}, {1112,1216}, {1511,7687}, {6053,10264}, {11557,12358}
X(12900) = reflection of X(6723) in X(3628)
X(12900) = complement of X(6699)
X(12900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,113,6699), (5,1511,7687), (5972,7687,1511)
The reciprocal orthologic center of these triangles is X(10112).
X(12901) lies on these lines: {3,125}, {24,12295}, {36,12888}, {74,323}, {110,3520}, {113,378}, {146,5654}, {155,10620}, {186,10733}, {376,12319}, {511,12596}, {541,2935}, {1092,7723}, {1147,3357}, {1511,4550}, {2777,12084}, {3043,12270}, {3047,6241}, {3098,9976}, {3448,12118}, {5448,7728}, {5972,7526}, {6101,7689}, {6396,12892}, {6644,7687}, {7688,12661}, {9818,12900}, {10117,12085}, {10539,12292}, {10645,10663}, {10646,10664}, {10721,12086}, {11410,12168}, {11430,12228}, {11438,12236}, {11442,12383}, {11454,12273}, {11468,12284}, {11999,12163}
X(12901) = midpoint of X(i) and X(j) for these {i,j}: {3,12302}, {74,5504}, {155,10620}, {2935,12412}, {3448,12118}, {10117,12085}
X(12901) = reflection of X(i) in X(j) for these (i,j): (110,12038), (7689,12041), (7728,5448), (9927,125), (12893,3)
X(12901) = X(104)-of-Trinh-triangle if ABC is acute
The reciprocal orthologic center of these triangles is X(6102).
X(12902) lies on these lines: {2,11801}, {3,125}, {4,195}, {5,12383}, {20,10264}, {30,3448}, {68,11559}, {74,1657}, {110,381}, {113,3843}, {146,3627}, {382,5663}, {517,12407}, {542,1351}, {568,11562}, {578,11597}, {999,12904}, {1154,12281}, {1511,1656}, {1539,5076}, {1598,12140}, {1699,11699}, {1986,12173}, {2079,10413}, {2771,5691}, {2777,5073}, {2930,3818}, {2937,12289}, {3028,9655}, {3043,7547}, {3091,10272}, {3146,12317}, {3295,12896}, {3521,10116}, {3534,9140}, {3567,11561}, {3845,9143}, {3851,7687}, {5055,5972}, {5071,11694}, {5790,12778}, {5876,12273}, {5898,6288}, {5899,10117}, {6102,12270}, {6243,10628}, {6407,8994}, {7517,12412}, {7723,11898}, {8976,10819}, {9301,12501}, {9654,10088}, {9669,10091}, {10246,12261}, {10247,12898}, {10255,12118}, {10516,12584}, {10778,12773}, {11744,12315}, {11842,12201}, {11849,12334}, {11850,12358}, {11875,12466}, {11876,12467}, {11911,12790}, {11916,12803}, {11917,12804}, {11928,12889}, {11929,12890}, {11949,12894}, {11950,12895}, {12000,12905}, {12001,12906}
X(12902) = midpoint of X(3146) and X(12317)
X(12902) = reflection of X(i) in X(j) for these (i,j): (3,265), (20,10264), (110,10113), (146,3627), (382,10733), (399,4), (1657,74), (2930,3818), (2931,9927), (3534,9140), (5898,6288), (7728,12295), (7731,10263), (9143,3845), (10620,3448), (11562,11800), (12121,125), (12270,6102), (12273,5876), (12308,7728), (12315,11744), (12383,5), (12773,10778)
X(12902) = anticomplement of X(34153)
X(12902) = X(265)-of-X3-ABC-reflections-triangle
X(12902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (110,10113,381), (125,12121,3), (265,12121,125), (3830,12308,7728), (7728,12295,3830), (11562,11800,568), (12896,12903,3295)
The reciprocal orthologic center of these triangles is X(6102).
X(12903) lies on the Johnson-Yff-inner-circle and these lines: {1,265}, {5,10091}, {12,110}, {30,10065}, {35,12121}, {56,125}, {67,1469}, {74,7354}, {113,10895}, {146,5229}, {388,3028}, {399,9654}, {495,10066}, {496,11801}, {498,1511}, {542,611}, {1112,11392}, {1317,10778}, {1388,11735}, {1478,5663}, {1479,10113}, {2771,10057}, {2777,10060}, {2854,12588}, {2931,9659}, {2948,9578}, {3023,11005}, {3031,9552}, {3043,9