X1879

ZOSMA TRANSFORM OF X563

X1879 = crosssum of X6 and X156
< 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, 13 }: Central Line L(6, 13) { 4, 96 }: Central Line L(4, 96) { 53, 235 }: Central Line L(53, 235) { 5, 570 }: Central Line L(5, 570) { 230, 428 }: Central Line L(230, 428) { 233, 566 }: Central Line L(233, 566) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_4 = ORTHOCENTER (0.6122, 0.3958) X_96 = ISOGONAL CONJUGATE OF X(52) (-0.0943, -0.0197) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_235 = -CEVA CONJUGATE OF X(185) (0.6375, 0.4618) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_570 = ORTHOGONAL OF X(52) (0.5652, 0.2098) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_233 = -CEVA CONJUGATE OF X(140) (0.5475, 0.2218) X_566 = HARMONIC OF X(50) (0.5516, 0.1872) X_1879 = ZOSMA TRANSFORM OF X(563) (0.5328, 0.3490) A B C X6 X13 X4 X96 X53 X235 X5 X570 X230 X428 X233 X566 X1879 (a, b, c) = (5, 6, 7) | AB = 1

X1879 (ZOSMA TRANSFORM OF X563) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((y + z) \sec A : (z + x) \sec B : (x + y) \sec C\), where \(x : y : z\) = X563
Barycentrics: \((y + z) \tan A : (z + x) \tan B : (x + y) \tan C\), where \(x : y : z\) = X563
Search Value (6, 9, 13): \(-7.457880200669\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sin A \cos(2B - 2C) : :\)

▸ Incident Central Lines7 lines

{4, 96}, {5, 570}, {6, 13}, {53, 235}, {230, 428}, {233, 566}, {1598, 1609}

▸ Functional Relations2 relations