X677

TRILINEAR POLE OF LINE X3X_101

X677 = isogonal conjugate of X676
< 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) { 521, 651 }: Central Line L(521, 651) { 103, 901 }: Central Line L(103, 901) { 59, 1813 }: Central Line L(59, 1813) { 765, 1332 }: Central Line L(765, 1332) { 518, 1814 }: Central Line L(518, 1814) { 1252, 1331 }: Central Line L(1252, 1331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_1813 = INVERSE MIMOSA TRANSFORM OF X(650) (-0.1088, 0.3999) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_1332 = ORTHOCORRESPONDENT OF X(100) (-0.2317, 0.1866) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1814 = INVERSE MIMOSA TRANSFORM OF X(672) (0.8952, -0.0254) X_1252 = ISOGONAL CONJUGATE OF X(1086) (0.4699, 0.3541) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_677 = TRILINEAR POLE OF LINE X(3)X(101) (1.3200, 0.4790) A B C X676 X521 X651 X103 X901 X59 X1813 X765 X1332 X518 X1814 X1252 X1331 X677 (a, b, c) = (5, 6, 7) | AB = 1

X677 (TRILINEAR POLE OF LINE X3X_101) 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 \(f(a,b,c) = a/{(b - c)[b^{3} + c^{3} - 2a^{3} + (b + c)(a^{2} - bc)]}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-3.168417854778\)

X677 lies on the MacBeath circumconic.

▸ Incident Central Lines9 lines

{59, 1813}, {103, 901}, {518, 1814}, {521, 651}, {765, 1332}, {883, 2398}, {1252, 1331}, {1815, 2340}, {2323, 2338}

▸ Functional Relations2 relations