X1831

ZOSMA TRANSFORM OF X12

X1831 = crosspoint of X4 and X270
< 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, 80 }: Central Line L(4, 80) { 28, 501 }: Central Line L(28, 501) { 33, 1697 }: Central Line L(33, 1697) { 225, 1871 }: Central Line L(225, 1871) { 1829, 1842 }: Central Line L(1829, 1842) { 1835, 1838 }: Central Line L(1835, 1838) 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_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_501 = MIQUEL ASSOCIATE OF INCENTER (0.5444, 0.1612) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5449, 0.1845) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1871 = ZOSMA TRANSFORM OF X(498) (0.6168, 0.4040) X_1829 = ZOSMA TRANSFORM OF X(10) (0.6233, 0.4161) X_1842 = ZOSMA TRANSFORM OF X(72) (0.6364, 0.4517) X_1835 = ZOSMA TRANSFORM OF X(30) (0.6564, 0.6795) X_1838 = ZOSMA TRANSFORM OF X(35) (0.6188, 0.4218) X_1831 = ZOSMA TRANSFORM OF X(12) (0.6144, 0.3920) A B C X4 X270 X80 X28 X501 X33 X1697 X225 X1871 X1829 X1842 X1835 X1838 X1831 (a, b, c) = (5, 6, 7) | AB = 1

X1831 (ZOSMA TRANSFORM OF X12) 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,\(x : y : z\) = X12
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X12
Search Value (6, 9, 13): \(-104.620852749520\)
▸ Incident Central Lines8 lines

{4, 80}, {28, 501}, {33, 1697}, {225, 1871}, {1829, 1842}, {1835, 1838}, {1839, 1858}, {1844, 1870}

▸ Functional Relations2 relations