X1026

INTERSECTION OF LINES X1X_2 AND X100X_101

X1026 = crosssum of X513 and X659
< 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, 2 }: Nagel Line { 100, 101 }: Central Line L(100, 101) { 664, 668 }: Central Line L(664, 668) { 55, 1083 }: Central Line L(55, 1083) { 666, 1027 }: Central Line L(666, 1027) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1027 = INTERSECTION OF LINES X(1)X(514) AND X(6)X(513) (1.0130, 0.0424) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4771, 0.1213) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_1026 = INTERSECTION OF LINES X(1)X(2) AND X(100)X(101) (4.1429, 3.7326) A B C X1027 X1 X2 X100 X101 X664 X668 X55 X1083 X666 X1026 (a, b, c) = (5, 6, 7) | AB = 1

X1026 (INTERSECTION OF LINES X1X_2 AND X100X_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 \(f(a,b,c) = [b^{2} + c^{2} - a(b + c)]/(b - c)\)
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): \(-6.820212003964\)
▸ Incident Central Lines5 lines

{1, 2}, {55, 1083}, {100, 101}, {664, 668}, {666, 1027}

▸ Functional Relations4 relations