X1876

ZOSMA TRANSFORM OF X516

X1876 = midpoint of X65 and X1456
< 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) { 65, 1456 }: Central Line L(65, 1456) { 4, 7 }: Central Line L(4, 7) { 6, 19 }: Central Line L(6, 19) { 25, 57 }: Central Line L(25, 57) { 33, 354 }: Central Line L(33, 354) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1456 = -BETH CONJUGATE OF X(516) (0.7238, 1.0576) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_354 = WEILL POINT (0.5823, 0.2533) X_1876 = ZOSMA TRANSFORM OF X(516) (0.6639, 0.6754) A B C X65 X1456 X4 X7 X6 X19 X25 X57 X33 X354 X1876 (a, b, c) = (5, 6, 7) | AB = 1

X1876 (ZOSMA TRANSFORM OF X516) 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,\(x : y : z\) = X516
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X516
Search Value (6, 9, 13): \(0.159853065072\)
▸ Incident Central Lines26 lines

{1, 1037}, {4, 7}, {6, 19}, {25, 57}, {28, 1170}, {33, 354}, {59, 517}, {72, 475}, {108, 840}, {196, 1851}, {225, 1887}, {226, 427}, {235, 1210}, {242, 653}, {278, 1002}, {428, 553}, {513, 1835}, {518, 1861}, {614, 3195}, {851, 1465}, {950, 1885}, {1011, 1214}, {1020, 1736}, {1068, 1872}, {1458, 2356}, {1471, 2212}

▸ Functional Relations3 relations