X1842

ZOSMA TRANSFORM OF X72

X1842 = X4-Ceva conjugate of X1834
< 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, 9 }: Orthocenter–Spieker Line { 28, 36 }: Central Line L(28, 36) { 51, 65 }: Central Line L(51, 65) { 34, 207 }: Central Line L(34, 207) { 25, 225 }: Central Line L(25, 225) { 33, 976 }: Central Line L(33, 976) 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_1834 = ZOSMA TRANSFORM OF X(28) (0.5987, 0.2534) X_9 = MITTENPUNKT (0.5110, 0.1615) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_976 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(38) (0.5520, 0.2143) X_1842 = ZOSMA TRANSFORM OF X(72) (0.6364, 0.4517) A B C X4 X1834 X9 X28 X36 X51 X65 X34 X207 X25 X225 X33 X976 X1842 (a, b, c) = (5, 6, 7) | AB = 1

X1842 (ZOSMA TRANSFORM OF X72) 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,\(x : y : z\) = X72
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X72
Search Value (6, 9, 13): \(-0.600096067374\)
▸ Incident Central Lines12 lines

{4, 9}, {25, 225}, {28, 36}, {29, 1848}, {33, 976}, {34, 207}, {51, 65}, {92, 1891}, {278, 1420}, {1737, 1782}, {1829, 1831}, {1878, 1888}

▸ Functional Relations3 relations