X3899

X549com[INVERSE(n(4th EULER TRIANGLE))]

< 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, 21 }: Central Line L(1, 21) { 210, 381 }: Central Line L(210, 381) { 484, 997 }: Central Line L(484, 997) { 960, 1698 }: Central Line L(960, 1698) { 165, 2800 }: Central Line L(165, 2800) { 8, 3583 }: Central Line L(8, 3583) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_997 = MIDPOINT OF X(1) AND X(200) (0.5053, 0.1685) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_2800 = ISOGONAL CONJUGATE OF X(2716) (0.2444, 0.7084) X_8 = NAGEL POINT (0.4694, 0.1333) X_3583 = INTERSECTION OF LINES X(1)X(4) AND X(11)X(30) (0.1361, -1.4997) X_3899 = com[INVERSE(n(4th EULER TRIANGLE))] (0.4599, 0.0866) A B C X1 X21 X210 X381 X484 X997 X960 X1698 X165 X2800 X8 X3583 X3899 (a, b, c) = (5, 6, 7) | AB = 1

X3899 (X549com[INVERSE(n(4th 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 \(f(a,b,c) = a(2b^{3} + 2c^{3} - 2a^{2}b - 2a^{2}c + 3abc)\)
Search Value (6, 9, 13): \(5.115872003456\)
▸ Incident Central Lines12 lines

{1, 21}, {8, 3583}, {65, 3624}, {72, 3586}, {165, 2800}, {210, 381}, {392, 3742}, {484, 997}, {960, 1698}, {1376, 3245}, {2802, 3681}, {3057, 3633}