X1998

ORTHOCORRESPONDENT OF X9

< 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) { 1, 2 }: Nagel Line { 57, 1004 }: Central Line L(57, 1004) { 63, 1005 }: Central Line L(63, 1005) { 100, 1445 }: Central Line L(100, 1445) { 224, 1467 }: Central Line L(224, 1467) { 273, 1897 }: Central Line L(273, 1897) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1004 = INTERCEPT OF EULER LINE AND LINE X(7)X(100) (0.5701, 0.2854) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1005 = INTERCEPT OF EULER LINE AND LINE X(9)X(100) (0.5199, 0.1541) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1445 = -BETH CONJUGATE OF X(344) (0.6570, 0.3740) X_224 = -CEVA CONJUGATE OF X(63) (1.2479, 0.4419) X_1467 = -BETH CONJUGATE OF X(938) (0.6380, 0.3556) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_1897 = ZOSMA TRANSFORM OF X(1054) (0.4360, 0.5756) X_1998 = ORTHOCORRESPONDENT OF X(9) (0.7061, 0.3652) A B C X1 X2 X57 X1004 X63 X1005 X100 X1445 X224 X1467 X273 X1897 X1998 (a, b, c) = (5, 6, 7) | AB = 1

X1998 (ORTHOCORRESPONDENT OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X9
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.681388993189\)
▸ Incident Central Lines7 lines

{1, 2}, {57, 1004}, {63, 1005}, {100, 1445}, {224, 1467}, {273, 1897}, {1331, 1743}