X2885

COMPLEMENTARY CONJUGATE OF X8

X2885 = complementary conjugate of X8
< 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, 121 }: Central Line L(5, 121) { 10, 496 }: Central Line L(10, 496) { 2, 1222 }: Central Line L(2, 1222) { 45, 1213 }: Central Line L(45, 1213) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_2 = CENTROID (0.5374, 0.2000) X_1222 = ISOGONAL CONJUGATE OF X(1201) (0.5108, 0.1870) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_2885 = COMPLEMENTARY CONJUGATE OF X(8) (0.6138, 0.2371) A B C X5 X121 X10 X496 X2 X1222 X45 X1213 X2885 (a, b, c) = (5, 6, 7) | AB = 1

X2885 (COMPLEMENTARY CONJUGATE OF X8) 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 \(f(a,b,c) = bc(b + c - 3a)(b^{3} + c^{3} + ab^{2} + ac^{2} - 3b^{2}c - 3bc^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.290560784480\)
▸ Incident Central Lines4 lines

{2, 1222}, {5, 121}, {10, 496}, {45, 1213}

▸ Functional Relations2 relations