X3349

INTERSECTION OF LINES X3X_2130 AND X4X_2131

X3349 = X6-cross conjugate of X3343
< 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) { 3, 2130 }: Central Line L(3, 2130) { 4, 2131 }: Central Line L(4, 2131) { 223, 3341 }: Central Line L(223, 3341) { 9, 3351 }: Central Line L(9, 3351) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3343 = -CEVA CONJUGATE OF X(1073) (0.6143, 0.3503) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_3341 = -CEVA CONJUGATE OF X(282) (0.6101, 0.5135) X_9 = MITTENPUNKT (0.5110, 0.1615) X_3351 = -CEVA CONJUGATE OF X(3342) (0.6100, 0.2900) X_3349 = INTERSECTION OF LINES X(3)X(2130) AND X(4)X(2131) (0.5517, 0.2144) A B C X6 X3343 X3 X2130 X4 X2131 X223 X3341 X9 X3351 X3349 (a, b, c) = (5, 6, 7) | AB = 1

X3349 (INTERSECTION OF LINES X3X_2130 AND X4X_2131) 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 \(f(a,b,c) = a[x + y + z - 2yz(y + z - x)/(y^{2} + z^{2} - x^{2})]^{- 1}\), where x : y : \(z = 1/(b^{2} + c^{2} - a^{2}) : 1/(c^{2} + a^{2} - b^{2}) : 1/(a^{2} + b^{2} - c^{2})\) (M. Iliev, 10/27/08)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.199660384570\)

X3349 lies on the Thomson cubic.

▸ Incident Central Lines4 lines

{3, 2130}, {4, 2131}, {9, 3351}, {223, 3341}

▸ Functional Relations5 relations