X3255

INTERSECTION OF X104X_551 AND X390X_1392

X3255 = isogonal conjugate of X3256
< 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) { 105, 551 }: Central Line L(105, 551) { 758, 1000 }: Central Line L(758, 1000) { 390, 1392 }: Central Line L(390, 1392) { 527, 2346 }: Central Line L(527, 2346) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3256 = ISOGONAL CONJUGATE OF X(3255) (0.5838, 0.2559) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_1000 = ISOGONAL CONJUGATE OF X(999) (0.5463, 0.1961) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_1392 = ISOGONAL CONJUGATE OF X(1388) (0.6149, 0.4463) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) X_2346 = -ISOCONJUGATE OF X(1475) (0.5596, 0.2138) X_3255 = INTERSECTION OF X(104)X(551) AND X(390)X(1392) (0.5578, 0.2112) A B C X3256 X105 X551 X758 X1000 X390 X1392 X527 X2346 X3255 (a, b, c) = (5, 6, 7) | AB = 1

X3255 (INTERSECTION OF X104X_551 AND X390X_1392) 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 \(f(a,b,c) = bc(b + c - a)/(bc + (b + c - a)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.533460163977\)
▸ Incident Central Lines4 lines

{105, 551}, {390, 1392}, {527, 2346}, {758, 1000}

▸ Functional Relations1 relation