X1875

ZOSMA TRANSFORM OF X515

X1875 = midpoint of X1785 and X1845
< 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) { 1785, 1845 }: Central Line L(1785, 1845) { 25, 34 }: Central Line L(25, 34) { 4, 65 }: Central Line L(4, 65) { 1, 945 }: Central Line L(1, 945) { 108, 953 }: Central Line L(108, 953) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1785 = MIMOSA TRANSFORM OF X(1295) (0.7297, 0.8635) X_1845 = ZOSMA TRANSFORM OF X(80) (0.5417, 0.5181) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1 = INCENTER (0.5714, 0.2333) X_945 = ISOGONAL CONJUGATE OF X(944) (0.6020, 0.4506) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_953 = ISOGONAL CONJUGATE OF X(952) (0.0000, 0.2041) X_1875 = ZOSMA TRANSFORM OF X(515) (0.6357, 0.6908) A B C X1785 X1845 X25 X34 X4 X65 X1 X945 X108 X953 X1875 (a, b, c) = (5, 6, 7) | AB = 1

X1875 (ZOSMA TRANSFORM OF X515) 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,\(x : y : z\) = X515
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X515
Search Value (6, 9, 13): \(0.100972480078\)
▸ Incident Central Lines13 lines

{1, 945}, {4, 65}, {25, 34}, {108, 953}, {225, 1829}, {278, 957}, {513, 1835}, {517, 1361}, {859, 1465}, {1119, 1122}, {1400, 1841}, {1452, 1454}, {1825, 1900}

▸ Functional Relations4 relations