X956

INTERSECTION OF LINES X1X_6 AND X3X_8

X956 = X55-of-inner-Garcia-triangle
< 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) { 55, 993 }: Central Line L(55, 993) { 1, 6 }: Incenter–Symmedian Line { 3, 8 }: Central Line L(3, 8) { 10, 56 }: Central Line L(10, 56) { 21, 145 }: Central Line L(21, 145) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) 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_8 = NAGEL POINT (0.4694, 0.1333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_956 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(8) (0.4790, 0.1235) A B C X55 X993 X1 X6 X3 X8 X10 X56 X21 X145 X956 (a, b, c) = (5, 6, 7) | AB = 1

X956 (INTERSECTION OF LINES X1X_6 AND X3X_8) 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 \(f(a,b,c) = a^{3} - a(b - c)^{2} - 2bc(b + c)\)
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): \(4.929739666792\)
▸ Linear Combinations1 combination
▸ Incident Central Lines12 lines

{1, 6}, {2, 495}, {3, 8}, {10, 56}, {21, 145}, {55, 519}, {63, 517}, {183, 668}, {210, 997}, {333, 859}, {388, 442}, {452, 1058}

▸ Functional Relations4 relations