X3494

INTERSECTION OF LINES X1X_87 AND X3X_2053

X3494 = isogonal conjugate of X3502
< 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) { 1, 87 }: Central Line L(1, 87) { 3, 2053 }: Central Line L(3, 2053) { 32, 2319 }: Central Line L(32, 2319) { 384, 3502 }: Central Line L(384, 3502) { 3491, 3501 }: Central Line L(3491, 3501) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3502 = ISOGONAL CONJUGATE OF X(3494) (0.6508, 0.3268) X_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2053 = -ISOCONJUGATE OF X(1423) (0.4486, 0.1337) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2319 = -ISOCONJUGATE OF X(1403) (0.4044, 0.1080) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_3491 = INTERSECTION OF LINES X(1)X(295) AND X(4)X(69) (0.5262, 0.2536) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) X_3494 = INTERSECTION OF LINES X(1)X(87) AND X(3)X(2053) (0.4381, 0.1402) A B C X3502 X1 X87 X3 X2053 X32 X2319 X384 X3491 X3501 X3494 (a, b, c) = (5, 6, 7) | AB = 1

X3494 (INTERSECTION OF LINES X1X_87 AND X3X_2053) 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 \(f(a,b,c) = (a^{2} + b^{2} + c^{2} - ab - ac + bc)/(ab + ac - bc) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.088243384467\)

X3494 lies on the cubic Z(X384).

▸ Incident Central Lines5 lines

{1, 87}, {3, 2053}, {32, 2319}, {384, 3502}, {3491, 3501}

▸ Functional Relations1 relation