X1901

ZOSMA TRANSFORM OF X1172

X1901 = X653-Ceva conjugate of X523
< 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) { 4, 6 }: Van Aubel Line { 9, 46 }: Central Line L(9, 46) { 12, 71 }: Central Line L(12, 71) { 115, 117 }: Central Line L(115, 117) { 37, 226 }: Central Line L(37, 226) { 30, 284 }: Central Line L(30, 284) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_1901 = ZOSMA TRANSFORM OF X(1172) (0.6043, 0.3127) A B C X653 X523 X4 X6 X9 X46 X12 X71 X115 X117 X37 X226 X30 X284 X1901 (a, b, c) = (5, 6, 7) | AB = 1

X1901 (ZOSMA TRANSFORM OF X1172) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((y + z) \sec A : :\), where \(x : y : z\) =X1172
Barycentrics: \((b + c) (2 a^{4} + a^{3} (b + c) - a^{2} (b - c)^{2} - a (b - c)^{2} (b + c) - (b^{2} - c^{2})^{2}) : :\)
Search Value (6, 9, 13): \(-0.467823665424\)
▸ Incident Central Lines21 lines

{4, 6}, {5, 579}, {7, 857}, {9, 46}, {12, 71}, {19, 1836}, {30, 284}, {37, 226}, {65, 1826}, {72, 594}, {115, 117}, {198, 851}, {208, 429}, {219, 1478}, {329, 1211}, {377, 965}, {430, 1827}, {583, 1713}, {946, 1108}, {950, 1100}, {1146, 1845}

▸ Functional Relations4 relations