X3499

INTERSECTION OF LINES X3X_695 AND X6X_76

X3499 = vertex conjugate of PU(141)
< 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) { 6, 76 }: Central Line L(6, 76) { 3, 695 }: Central Line L(3, 695) { 2076, 2916 }: Central Line L(2076, 2916) 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_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X(39) (1.3982, 1.5854) X_2916 = TANGENTIAL-ISOGONAL CONJUGATE OF X(2) (0.4656, -0.0146) X_3499 = INTERSECTION OF LINES X(3)X(695) AND X(6)X(76) (0.6625, 0.3232) A B C X6 X76 X3 X695 X2076 X2916 X3499 (a, b, c) = (5, 6, 7) | AB = 1

X3499 (INTERSECTION OF LINES X3X_695 AND X6X_76) 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 \(f(a,b,c) = a[a^{4}(b^{4} + b^{2}c^{2} + c^{4}) + a^{2}b^{2}c^{2}(b^{2} + c^{2}) - b^{4}c^{4}] (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.003118732630\)

X3499 lies on the cubic Z(X384).

▸ Incident Central Lines3 lines

{3, 695}, {6, 76}, {2076, 2916}

▸ Functional Relations2 relations