X3832

X3090com(EULER TRIANGLE)

X3832 = {X1131,X1132}-harmonic conjugate of X6
< 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) { 1131, 1132 }: Central Line L(1131, 1132) { 2, 3 }: Euler Line { 12, 390 }: Central Line L(12, 390) { 145, 946 }: Central Line L(145, 946) { 6, 1131 }: Central Line L(6, 1131) { 8, 1699 }: Central Line L(8, 1699) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1131 = ARCTAN(2) KIEPERT POINT (0.5904, 0.2888) X_1132 = ARCTAN(-2) KIEPERT POINT (0.8864, -0.3774) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_8 = NAGEL POINT (0.4694, 0.1333) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_3832 = com(EULER TRIANGLE) (0.5802, 0.3118) A B C X6 X1131 X1132 X2 X3 X12 X390 X145 X946 X8 X1699 X3832 (a, b, c) = (5, 6, 7) | AB = 1

X3832 (X3090com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 3a^{4} - 5b^{4} - 5c^{4} + 2a^{2}b^{2} + 2a^{2}c^{2} + 10b^{2}c^{2}\)
Search Value (6, 9, 13): \(-2.116910180891\)
▸ Incident Central Lines14 lines

{2, 3}, {6, 1131}, {8, 1699}, {11, 3600}, {12, 390}, {64, 3066}, {145, 946}, {355, 3621}, {489, 3595}, {490, 3593}, {515, 3622}, {962, 3617}, {3085, 3583}, {3086, 3585}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X3832 has Shinagawa coefficients \((1, 4)\).