X965

INTERSECTION OF LINES X2X_6 AND X3X_9

< 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, 9 }: Central Line L(3, 9) { 37, 78 }: Central Line L(37, 78) { 10, 219 }: Central Line L(10, 219) { 284, 405 }: Central Line L(284, 405) { 19, 960 }: Central Line L(19, 960) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_19 = CLAWSON POINT (0.6246, 0.4244) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_965 = INTERSECTION OF LINES X(2)X(6) AND X(3)X(9) (0.5133, 0.1741) A B C X2 X6 X3 X9 X37 X78 X10 X219 X284 X405 X19 X960 X965 (a, b, c) = (5, 6, 7) | AB = 1

X965 (INTERSECTION OF LINES X2X_6 AND X3X_9) 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 \(f(a,b,c) = a^{4} - a^{3}(b + c) - a^{2}(b^{2} + c^{2}) + a(b + c)^{3} + 2bc(b + c)^{2}\)
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): \(3.237439266719\)
▸ Incident Central Lines8 lines

{2, 6}, {3, 9}, {10, 219}, {19, 960}, {37, 78}, {48, 958}, {284, 405}, {474, 579}