X3898

X547com[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) { 55, 214 }: Central Line L(55, 214) { 10, 496 }: Central Line L(10, 496) { 210, 392 }: Central Line L(210, 392) { 517, 549 }: Central Line L(517, 549) { 2, 2802 }: Central Line L(2, 2802) 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_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_2 = CENTROID (0.5374, 0.2000) X_2802 = ISOGONAL CONJUGATE OF X(2718) (1.0529, -0.0806) X_3898 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5435, 0.1966) A B C X1 X21 X55 X214 X10 X496 X210 X392 X517 X549 X2 X2802 X3898 (a, b, c) = (5, 6, 7) | AB = 1

X3898 (X547com[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 \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c + 6abc)\)
Search Value (6, 9, 13): \(2.546699382957\)
▸ Incident Central Lines13 lines

{1, 21}, {2, 2802}, {10, 496}, {55, 214}, {65, 3636}, {72, 3635}, {145, 3678}, {210, 392}, {517, 549}, {960, 3244}, {997, 3158}, {1125, 3057}, {3616, 3754}