X3955

X1848com[INVERSE(n(ORTHIC TRIANGLE))]

X3955 = crosssum of the polar conjugates of PU(6)
< 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) { 3, 73 }: Central Line L(3, 73) { 57, 182 }: Central Line L(57, 182) { 63, 184 }: Central Line L(63, 184) { 228, 295 }: Central Line L(228, 295) { 1, 987 }: Central Line L(1, 987) { 36, 1401 }: Central Line L(36, 1401) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_1 = INCENTER (0.5714, 0.2333) X_987 = ISOGONAL CONJUGATE OF X(986) (0.5829, 0.2572) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1401 = -BETH CONJUGATE OF X(38) (0.6188, 0.3077) X_3955 = com[INVERSE(n(ORTHIC TRIANGLE))] (0.5145, 0.1142) A B C X3 X73 X57 X182 X63 X184 X228 X295 X1 X987 X36 X1401 X3955 (a, b, c) = (5, 6, 7) | AB = 1

X3955 (X1848com[INVERSE(n(ORTHIC TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(a^{2} + bc)(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(11.394593085644\)
▸ Incident Central Lines19 lines

{1, 987}, {3, 73}, {36, 1401}, {57, 182}, {63, 184}, {72, 1437}, {110, 3219}, {171, 2330}, {219, 3167}, {228, 295}, {293, 1214}, {394, 3781}, {436, 1948}, {511, 2003}, {611, 1460}, {982, 1428}, {1409, 2359}, {1707, 2175}, {3292, 3690}

▸ Functional Relations1 relation

  • X3955 = crosssum of the polar conjugates of PU(6)