X2476

INVERSE-IN-ORTHOCENTROIDAL-CIRCLE OF X21

X2476 = inverse-in-orthocentroidal-circle of X21
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3 }: Euler Line { 8, 12 }: Central Line L(8, 12) { 100, 498 }: Central Line L(100, 498) { 145, 495 }: Central Line L(145, 495) { 10, 908 }: Central Line L(10, 908) { 264, 1441 }: Central Line L(264, 1441) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_1441 = -BETH CONJUGATE OF X(313) (0.5459, 0.2242) X_2476 = INVERSE-IN-ORTHOCENTROIDAL-CIRCLE OF X(21) (0.5445, 0.2185) A B C X2 X3 X4 X8 X12 X100 X498 X145 X495 X10 X908 X264 X1441 X2476 (a, b, c) = (5, 6, 7) | AB = 1

X2476 (INVERSE-IN-ORTHOCENTROIDAL-CIRCLE OF X21) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[abc(b + c) - (b^{2} - c^{2})^{2} + a^{2}(b^{2} + bc + c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.145407353105\)
▸ Incident Central Lines74 lines

{1, 3822}, {2, 3}, {6, 5949}, {8, 12}, {10, 908}, {11, 3486}, {63, 5705}, {65, 3838}, {78, 5219}, {81, 5292}, {100, 498}, {115, 5283}, {119, 5554}, {145, 495}, {149, 3295}, {226, 3868}, {264, 1441}, {484, 1698}, {496, 3622}, {499, 5253}, {515, 3897}, {946, 3877}, {958, 5080}, {986, 3120}, {993, 3585}, {1150, 1330}, {1210, 5249}, {1213, 5036}, {1329, 3614}, {1478, 2975}, {1479, 1621}, {1699, 5250}, {1834, 5718}, {1858, 3812}, {1901, 5742}, {1993, 5707}, {2287, 5747}, {2292, 3944}, {2550, 5552}, {2651, 5278}, {2893, 5736}, {3006, 4385}, {3085, 3434}, {3193, 5713}, {3219, 5791}, {3241, 3813}, {3583, 5248}, {3624, 3825}, {3679, 3984}, {3695, 4671}, {3698, 5123}, {3705, 4968}, {3753, 5887}, {3767, 5276}, {3772, 5262}, {3811, 5178}, {3816, 5550}, {3824, 5439}, {3826, 5698}, {3914, 5530}, {3947, 4847}, {4299, 5303}, {4511, 5794}, {4853, 5726}, {4861, 5252}, {5175, 5703}, {5231, 5290}, {5330, 5603}, {5432, 6668}, {5587, 6261}, {5714, 5905}, {5883, 6701}, {5985, 6033}, {6284, 6690}

▸ Functional Relations1 relation

  • X2476 = inverse-in-orthocentroidal-circle of X21

Notes

As a point on the Euler line, X2476 has Shinagawa coefficients \((abc\$a\$ + 2S^{2}, 2S^{2})\)