X3507

INTERSECTION OF LINES X1X_2 AND X32X_2319

X3507 = X385-Ceva conjugate of X3508
< 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 { 32, 2319 }: Central Line L(32, 2319) { 511, 3512 }: Central Line L(511, 3512) { 694, 3508 }: Central Line L(694, 3508) { 3225, 3510 }: Central Line L(3225, 3510) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_3508 = INTERSECTION OF LINES X(1)X(6) AND X(76)X(1423) (2.7263, 2.7925) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2319 = -ISOCONJUGATE OF X(1403) (0.4044, 0.1080) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_3512 = ISOGONAL CONJUGATE OF X(3509) (0.9280, -0.1499) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_3225 = SS(a → bc) OF X(98) (1.1195, 0.2435) X_3510 = INTERSECTION OF LINES X(1)X(76) AND X(6)X(43) (1.7132, 1.1732) X_3507 = INTERSECTION OF LINES X(1)X(2) AND X(32)X(2319) (2.0184, 1.6510) A B C X385 X3508 X1 X2 X32 X2319 X511 X3512 X694 X3225 X3510 X3507 (a, b, c) = (5, 6, 7) | AB = 1

X3507 (INTERSECTION OF LINES X1X_2 AND X32X_2319) 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 \(f(a,b,c) = a^{3}(b + c) - (a^{2} + bc)(b^{2} + bc + c^{2}) + a(b + c)(b^{2} + c^{2}) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.652047248189\)

X3507 lies on the cubic Z(X385).

▸ Incident Central Lines5 lines

{1, 2}, {32, 2319}, {511, 3512}, {694, 3508}, {3225, 3510}

▸ Functional Relations1 relation