X954

INTERSECTION OF LINES X1X_6 AND X3X_7

X954 = isogonal conjugate of X955
< 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, 6 }: Incenter–Symmedian Line { 3, 7 }: Central Line L(3, 7) { 21, 144 }: Central Line L(21, 144) { 55, 226 }: Central Line L(55, 226) { 4, 390 }: Central Line L(4, 390) { 10, 480 }: Central Line L(10, 480) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_955 = ISOGONAL CONJUGATE OF X(954) (0.5804, 0.2446) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_4 = ORTHOCENTER (0.6122, 0.3958) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_480 = -CEVA CONJUGATE OF X(220) (0.4089, 0.0793) X_954 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(7) (0.5619, 0.2220) A B C X955 X1 X6 X3 X7 X21 X144 X55 X226 X4 X390 X10 X480 X954 (a, b, c) = (5, 6, 7) | AB = 1

X954 (INTERSECTION OF LINES X1X_6 AND X3X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{5} + (b + c)[2a^{2}(b^{2} + c^{2} - a^{2} + bc) - (b - c)^{2}(2bc + ab + ac)] : :\)
Search Value (6, 9, 13): \(1.864940916861\)
▸ Incident Central Lines9 lines

{1, 6}, {3, 7}, {4, 390}, {10, 480}, {21, 144}, {55, 226}, {142, 474}, {971, 1012}, {999, 1006}

▸ Functional Relations1 relation