About 85% of CTC cubics are circumcubics. These few do NOT pass through the A-vertex of ABC.

Knnn NOT through the A-vertex of ABC |
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Not through A of ABC (TCCT 6.1): K038, K048, K051, K075, K076, K077, K078, K079, K083B, K083C, K100, K138, K143B, K143C, K144, K153, K193, K203, K215, K219, K226, K244, K258, K265, K266, K271, K272, K277, K369, K401, K417, K418, K437, K456A, K458, K459, K460, K461, K462, K463, K508, K509, K511, K583, K591, K592, K593, K598, K600, K609, K645, K648, K649, K650, K651, K652, K656, K666, K667, K687, K700, K703, K722, K723, K725, K726, K727, K728, K733, K735, K736, K742, K752, K753, K758, K764, K765, K793, K794, K795, K796, K798, K799, K800, K801, K816, K817, K818, K833, K834, K837, K853, K858, K869, K870, K871, K872, K873, K874, K875, K876, K881, K882, K883, K884, K885, K886, K887, K888, K889, K890, K891, K892, K893, K894, K895, K896, K897, K898, K899B, K899C, K900, K903, K904, K905, K906, K907, K909, K910, K911, K912, K913, K920, K921, K934, K955, K957, K958, K966, K1063, K1064, K1070, K1071, K1083, K1084, K1085, K1091, K1092, K1094, K1095, K1096, K1098, K1099, K1102, K1103, K1105, K1106, K1107, K1108 |

Triangle: Knnn through its A-vertex |
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ABC reflected about O (TCCT 6.12): K004, K047, K069, K080, K426, K443, K566, K703, K706, K712, K814, K850, K918, K926 |

Ae, (CTC K798): K798 |

Ai, (CTC K798): K798 |

anticomplementary (TCCT 6.3): K007, K008, K034, K045, K080, K083A, K092, K133, K141, K142, K143A, K143B, K143C, K144, K146, K154, K170, K200, K210, K211, K235, K240, K242, K254, K264a, K264b, K279, K311, K355, K371, K377, K425, K449, K455, K548, K605, K610, K611, K617, K659, K753, K860, K985, K998, K1000, K1002, K1004, K1037, K1053a, K1053b, K1078 |

anti first-Brocard (see ETC X(5939)): K699, K740 |

anti first-Euler: K080 |

anti fourth-Brocard (CTC): K640 |

Apus (see ETC X(5584)): K009, K172 |

Ara (see ETC X(5594) / excentral of tangential: K174 |

Aries ETC X(5596)): K075, K191 |

Caelum / fifth mixitilinear (see ETC X(5603)): K201, K830, K831 |

Carnot / Johnson (reflection of ABC about X(5). MathWorld): K026, K044, K465, K526, K562, K725, K1095 |

centers of the Apollonius circles: K024, K147, K148, K149, K151, K191, K192, K214, K229, K604, K608, K634, K635, K734, K740, K1072 |

circum-medial (TCCT 6.19): K794, K959 |

circumnormal (TCCT 6.29): K003, K009, K227A, K361, K373, K404, K405, K519, K664, K725, K735, K736, K931 |

circum-orthic (TCCT 6.20): K110A, K158, K580, K919 |

circum-symmedial: K726 |

circumtangential (TCCT 6.28): K024, K078, K085, K098, K105, K403, K409, K686, K723, K726, K727, K728, K734, K735, K896, K902, K905, K1063, K1064, K1098 |

complement of Stammler (see X(6070)): K741 |

cuspes of Steiner deltoid (see CTC Q000) / 1st Steiner equilateral (see ETC X(6070)): K071, K244, K648, K649, K650, K651, K652 |

Euler (TCCT 6.11): K026 |

excentral of Thomson (CTC Q113): K078, K615, K763, K764, K765, K834 |

excentral (TCCT 6.7): K001, K002, K003, K004, K005, K006, K020, K021, K029, K030, K031, K035, K077, K078, K100, K102, K109, K128, K129a, K129b, K130, K152, K156, K158, K169, K173, K227A, K227B, K227C, K243, K258, K269, K270, K282, K316, K326, K343, K351, K364, K410, K414, K417, K422, K423, K424a, K424b, K434, K456A, K456B, K456C, K502, K585, K609, K655, K661, K668, K692, K695, K704, K717, K742, K751, K763, K800, K832, K837, K858, K910, K911, K913, K951, K968, K1025, K1026, K1027, K1039, K1044, K1055, K1059, K1071, K1079, K1086 |

extangents (TCCT 6.17): K391, K750 |

extouch (TCCT 6.9): K033, K199, K200, K308, K338, K667, K692, K710, K901, K926 |

Feuerbach (TCCT 6.10): K877 |

first Brocard (CTC): K012, K017, K020, K153, K512, K545, K547, K548, K549, K550, K551, K552, K553 |

first circumperp (TCCT 6.21): K100 |

first Conway (see ETC X(7411)): K344 |

first isodynamic-Dao equilateral (see X(16802)): K262b |

first Morley adjunct (TCCT 6.30): K029, K227A, K584 |

first Morley (TCCT 6.25): K029, K227A, K584 |

first Neuberg (MathWorld): K422 |

first orthosymmedial (see ETC X(6792)): K055 |

first Sharygin (see ETC X(8229)): K960, K962 |

first Zaniah, see X(18214): K363 |

fourth Brocard / D-triangle (CTC) / Johnson (Quim Castellsaguer): K018, K539 |

Fuhrmann (TCCT 8.25): K028, K680, K800 |

Gemini 01: K317 |

Gemini 04: K132 |

Gemini 09: K134 |

Gemini 12: K328 |

Gemini 13: K366 |

Gemini 15: K345 |

Gemini 17: K010 |

Gemini 18: K198 |

Gemini 31: K1007 |

Gemini 32: K1020 |

Gemini 33: K131 |

Gemini 34: K155 |

Gemini 43: K644 |

Gemini 44: K794, K959 |

Gemini 107: K065, K068, K213, K287, K315, K398, K399, K400a, K400b |

Gemini 110: K124 |

Grebe (CTC K102): K102, K138, K177, K281, K642, K643, K644, K729, K731, K835 |

half altitude / mid-height (TCCT 6.38): K002, K122, K645, K752, K858 |

hexyl (TCCT 6.36): K004, K100, K736 |

Hutson intouch (see ETC X(5731)): K830 |

incentral (TCCT 6.6): K097, K101, K157, K175, K206, K215, K362, K511, K560, K632, K672, K749, K761, K770, K774, K861, K927, K992, K1015, K1017, K1040, K1061 |

infinite altitude: K004, K127, K376, K405, K456A, K461, K615, K642, K650, K654, K758, K820, K838, K839, K840, K841, K842, K843, K844, K845, K846, K847, K848, K1100 |

inner Fermat (TCCT p178): K001 |

inner Garcia (see ETC X(5587)): K456A, K679 |

inner inscribed squares (MathWorld): K424a |

inner Napoleon (TCCT 6.32): K005, K463, K733 |

inner Vecten (MathWorld): K006 |

intouch / Gergonne(TCCT 6.8): K333, K360, K365, K561, K571, K572, K573, K574, K575, K577, K578, K631, K666, K713, K747, K830, K949, K964, K1058, K1059, K1078, K1082, K1089 |

inverse of ABC in the incircle: K666 |

isogonal of reflected 1st Brocard (CTC table 32): K020, K797 |

Kosnita (see ETC X(1658)): K388 |

Lemoine (MathWorld): K283 |

MacBeath (MathWorld): K028, K045, K555, K556, K562, K563, K583, K647, K674 |

Mandart-incircle (see ETC X(6018)): K925 |

medial of orthic / anti 2nd Conway (see X(11363)): K054, K350 |

medial of Thomson: K758, K765 |

medial (TCCT 6.2): K002, K009, K026, K038, K043, K051, K143A, K168, K177, K203, K207, K208, K219, K220, K226, K237, K251, K252, K253, K258, K259, K260, K265, K277, K284, K307, K321, K341a, K341b, K345, K357, K363, K376, K426, K446, K453, K472, K485, K489, K512, K557, K559, K564, K565, K567, K569, K570, K607, K612, K637, K663, K671, K752, K836, K856, K857, K879, K900, K924, K965, K996, K1012, K1035, K1036, K1038, K1045, K1060, K1068, K1077, K1095 |

orthic of anticomplementary: K111A |

orthic of intouch: K964 |

orthic-of-medial / anti-6th-mixtilinear (see X(11363)): K168, K418 |

orthic of orthic: K415 |

orthic of Thomson: K1093 |

orthic (TCCT 6.4): K006, K044, K049, K050, K051, K053A, K059, K110A, K170, K176, K181, K182, K209, K212, K233, K238, K329, K334, K337, K339, K350, K391, K415, K416, K429, K445, K475, K496, K517, K591, K691, K709, K718, K742, K807, K955, K969, K1087, K1088 |

orthocentroidal (see ETC X(5476)): K005, K295, K397, K733 |

outer Fermat (TCCT p178): K001 |

outer Garcia (see ETC X(5587)): K033 |

outer inscribed squares (MathWorld): K424b |

outer Napoleon (TCCT 6.31): K005, K463, K733 |

outer Vecten (MathWorld): K006 |

reflected 1st Brocard (CTC table 32): K020, K797 |

reflection A in BC: K001, K032, K115, K116, K117, K118, K119, K120, K216 |

refl X(1) in BC: K434 |

Schroeter (see ETC X(8286) / anticevian X(523) / diagonal triangle of Feuerbach quadrangle of ABC (see ETC X(10276)): K079, K237, K238, K239, K672, K877, K878 |

second Brocard (CTC): K018, K022, K053A, K083A, K509, K538, K793, K899A |

second circumperp (TCCT 6.22): K100, K318, K561, K838, K921 |

second Conway (see ETC X(9776)): K007, K028, K461, K651 |

second Euler (see ETC X(3758)): K044 |

second extouch (see ETC X(5927)): K880 |

second Fuhrmann: K028, K685, K800 |

second Hyacinth #24029: K418 |

second isodynamic-Dao equilateral (see X(16802)): K262a |

second Johnson-Yff (see X(10523)): K925 |

second Morley adjunct (MathWorld): K031, K227A |

second Morley (TCCT 6.26): K031, K227A |

second Neuberg (MathWorld): K422 |

second Sharygin (see ETC X(8229)): K961, K962 |

second Zaniah, see X(18214): K1077 |

Stammler (MathWorld): K297, K902 |

Steiner Deltoid NP touches (see CTC Q000) / 2nd Steiner equilateral (see ETC X6070)): K412, K583, K722 |

Steiner (MathWorld): K035, K242, K403, K568, K602, K1065 |

submedial (see ETC X(9813)): K281 |

symmedial (MathWorld): K102, K167, K215, K346, K367, K368, K390, K444, K579, K629, K659, K673, K693, K739, K790, K987, K1016, K1019, K1033, K1047, K1049 |

T(-2,1) (TCCT 6.41): K338 |

tangential of excentral: K343, K1060 |

tangential of Thomson: K172 |

tangential (TCCT 6.5): K075, K076, K108, K160, K161, K171, K172, K174, K175, K176, K177, K178, K179, K180, K236, K312, K389, K405, K428, K430, K431, K432, K478, K495, K622, K902, K904, K922, K999, K1001, K1003, K1005, K1042, K1043, K1054a, K1054b, K1056, K1067, K1104 |

third Brocard (CTC): K017, K020, K444, K546, K549 |

third extouch (see ETC X(5927)): K963 |

third Morley adjunct (MathWorld): K030, K227A |

third Morley (TCCT 6.27): K030, K227A |

Thomson (CTC K002): K002, K078, K138, K167, K172, K280, K297, K463, K581, K609, K615, K624, K625, K626, K703, K727, K758, K759, K760, K761, K764, K765, K804, K810, K833, K834, K903, K912, K913, K1093, K1095 |

Trinh (see ETC X(7688)): K488 |

vertex triangle ABC & intangents / Pelletier (TCCT 6.18): K925 |

Yff central (TCCT 6.37): K748 |