X1827

ZOSMA TRANSFORM OF X7

X1827 = crosspoint of X4 and X33
< 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, 7 }: Central Line L(4, 7) { 19, 25 }: Central Line L(19, 25) { 294, 1172 }: Central Line L(294, 1172) { 46, 1721 }: Central Line L(46, 1721) { 1425, 1547 }: Central Line L(1425, 1547) { 208, 1887 }: Central Line L(208, 1887) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_7 = GERGONNE POINT (0.5903, 0.2769) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1721 = MIMOSA TRANSFORM OF X(55) (0.6494, 0.4136) X_1425 = -BETH CONJUGATE OF X(201) (0.5904, 0.1922) X_1547 = ORTHOJOIN OF X(71) (0.6764, 1.0690) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_1887 = ZOSMA TRANSFORM OF X(946) (0.6088, 0.3521) X_1827 = ZOSMA TRANSFORM OF X(7) (0.6082, 0.3740) A B C X4 X33 X7 X19 X25 X294 X1172 X46 X1721 X1425 X1547 X208 X1887 X1827 (a, b, c) = (5, 6, 7) | AB = 1

X1827 (ZOSMA TRANSFORM OF X7) 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,\(x : y : z\) = X7
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X7
Search Value (6, 9, 13): \(8.626032777092\)
▸ Incident Central Lines9 lines

{4, 7}, {19, 25}, {46, 1721}, {208, 1887}, {294, 1172}, {430, 1856}, {1425, 1547}, {1828, 1843}, {1845, 1905}

▸ Functional Relations4 relations