X1007

INTERCEPT OF LINES X2X_6 AND X4X_99

X1007 = isotomic conjugate of X7612
< 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 { 4, 99 }: Central Line L(4, 99) { 305, 311 }: Central Line L(305, 311) { 316, 376 }: Central Line L(316, 376) { 315, 631 }: Central Line L(315, 631) 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_4 = ORTHOCENTER (0.6122, 0.3958) X_99 = STEINER POINT (0.1109, 0.4322) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_631 = 3/5*OG (0.5224, 0.1608) X_1007 = INTERCEPT OF LINES X(2)X(6) AND X(4)X(99) (0.7128, 0.3884) A B C X2 X6 X4 X99 X305 X311 X316 X376 X315 X631 X1007 (a, b, c) = (5, 6, 7) | AB = 1

X1007 (INTERCEPT OF LINES X2X_6 AND X4X_99) 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 \(f(a,b,c) = bc[a^{4} - 4a^{2}(b^{2} + c^{2}) + 3b^{4} - 2b^{2}c^{2} + 3c^{4}]\)
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): \(12.178227865681\)
▸ Incident Central Lines6 lines

{2, 6}, {4, 99}, {305, 311}, {315, 631}, {316, 376}, {317, 6353}

▸ Functional Relations4 relations