X871

ISOTOMIC CONJUGATE OF X869

X871 is the isotomic conjugate of X869.
< 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) { 76, 335 }: Central Line L(76, 335) { 2, 561 }: Central Line L(2, 561) { 75, 700 }: Central Line L(75, 700) { 86, 870 }: Central Line L(86, 870) { 675, 789 }: Central Line L(675, 789) { 310, 982 }: Central Line L(310, 982) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_2 = CENTROID (0.5374, 0.2000) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_700 = EVEN (- 4, - 1) INFINITY POINT (0.0346, -0.1027) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_870 = ISOGONAL CONJUGATE OF X(869) (0.5328, 0.2015) X_675 = TRILINEAR POLE OF LINE X(6)X(514) (0.9212, -0.1860) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_871 = ISOTOMIC CONJUGATE OF X(869) (0.4515, 0.1398) A B C X869 X76 X335 X2 X561 X75 X700 X86 X870 X675 X789 X310 X982 X871 (a, b, c) = (5, 6, 7) | AB = 1

X871 (ISOTOMIC CONJUGATE OF X869) 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 \(f(a,b,c) = 1/[a^{4}(b^{2} + c^{2} + bc)]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(4.944751352293\)
▸ Incident Central Lines6 lines

{2, 561}, {75, 700}, {76, 335}, {86, 870}, {310, 982}, {675, 789}

▸ Functional Relations1 relation