X3430

ISOGONAL CONJUGATE OF X3429

X3430 is the isogonal conjugate of X3429.
< 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) { 20, 1330 }: Central Line L(20, 1330) { 3, 6 }: Brocard Axis { 169, 936 }: Central Line L(169, 936) { 101, 1297 }: Central Line L(101, 1297) { 78, 1763 }: Central Line L(78, 1763) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_1763 = MIMOSA TRANSFORM OF X(326) (0.4019, -0.3639) X_3430 = ISOGONAL CONJUGATE OF X(3429) (0.3893, -0.0808) A B C X20 X1330 X3 X6 X169 X936 X101 X1297 X78 X1763 X3430 (a, b, c) = (5, 6, 7) | AB = 1

X3430 (ISOGONAL CONJUGATE OF X3429) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/x(3429) : :\)
Barycentrics: \(^{2}[a^{5} + a^{3}bc + a^{2}(b + c)(2b^{2} - bc + 2c^{2}) - a(b + c)^{2}(b^{2} - bc + c^{2}) - (b + c)(2b^{4} - b^{3}c + 2b^{2}c^{2} - bc^{3} + 2c^{4})] : : (E. Danneels)\)
Search Value (6, 9, 13): \(12.812793543031\)
▸ Incident Central Lines13 lines

{3, 6}, {20, 1330}, {72, 1782}, {78, 1763}, {101, 1297}, {169, 936}, {404, 1730}, {842, 2705}, {951, 1427}, {1293, 2842}, {1490, 1766}, {2360, 2915}, {2702, 2710}

▸ Functional Relations3 relations