X3314

INTERSECTION OF LINES X2X_6 AND X76X_115

X3314 = crosspoint of X327 and X1502
< 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) { 2, 6 }: Centroid–Symmedian Line { 3, 147 }: Central Line L(3, 147) { 76, 115 }: Central Line L(76, 115) { 315, 384 }: Central Line L(315, 384) { 982, 2887 }: Central Line L(982, 2887) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_2887 = COMPLEMENTARY CONJUGATE OF X(37) (0.4947, 0.1495) X_3314 = INTERSECTION OF LINES X(2)X(6) AND X(76)X(115) (0.4770, 0.1350) A B C X2 X6 X3 X147 X76 X115 X315 X384 X982 X2887 X3314 (a, b, c) = (5, 6, 7) | AB = 1

X3314 (INTERSECTION OF LINES X2X_6 AND X76X_115) 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 \(f(a,b,c) = bc[(b^{2} + c^{2})^{2} - b^{2}c^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.030634497676\)
▸ Incident Central Lines5 lines

{2, 6}, {3, 147}, {76, 115}, {315, 384}, {982, 2887}

▸ Functional Relations5 relations