X1389

ISOGONAL CONJUGATE OF X1385

X1389 is the isogonal conjugate of X1385.
< 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) { 5, 8 }: Central Line L(5, 8) { 65, 104 }: Central Line L(65, 104) { 21, 517 }: Central Line L(21, 517) { 79, 515 }: Central Line L(79, 515) { 7, 944 }: Central Line L(7, 944) { 80, 946 }: Central Line L(80, 946) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1385 = MIDPOINT OF INCENTER AND CIRCUMCENTER (0.5357, 0.1677) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_8 = NAGEL POINT (0.4694, 0.1333) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_7 = GERGONNE POINT (0.5903, 0.2769) X_944 = HOFSTADTER TRAPEZOID POINT (0.5306, 0.0708) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_1389 = ISOGONAL CONJUGATE OF X(1385) (0.5985, 0.3054) A B C X1385 X5 X8 X65 X104 X21 X517 X79 X515 X7 X944 X80 X946 X1389 (a, b, c) = (5, 6, 7) | AB = 1

X1389 (ISOGONAL CONJUGATE OF X1385) 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 \(f(a,b,c) = 1/[16(\operatorname{area} ABC)^{2} + a(a + b + c)(b^{2} + c^{2} - a^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.113088359144\)
▸ Incident Central Lines8 lines

{1, 1393}, {5, 8}, {7, 944}, {21, 517}, {65, 104}, {79, 515}, {80, 946}, {942, 1476}

▸ Functional Relations1 relation