X1911

TRILINEAR POLE OF PU(9)

X1911 = X741-Ceva conjugate of X292
< 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) { 42, 81 }: Central Line L(42, 81) { 6, 292 }: Central Line L(6, 292) { 1, 335 }: Central Line L(1, 335) { 86, 334 }: Central Line L(86, 334) { 172, 694 }: Central Line L(172, 694) { 238, 660 }: Central Line L(238, 660) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_1 = INCENTER (0.5714, 0.2333) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_660 = TRILINEAR POLE OF LINE X(1)X(39) (0.9483, -0.0755) X_1911 = TRILINEAR POLE OF PU(9) (1.0016, 0.0478) A B C X350 X42 X81 X6 X292 X1 X335 X86 X334 X172 X694 X238 X660 X1911 (a, b, c) = (5, 6, 7) | AB = 1

X1911 (TRILINEAR POLE OF PU(9)) 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 \(f(a,b,c) = a^{2}/(a^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.081079009980\)
▸ Incident Central Lines11 lines

{1, 335}, {6, 292}, {42, 81}, {86, 334}, {172, 694}, {238, 660}, {692, 1333}, {739, 813}, {875, 890}, {1403, 1407}, {1429, 1458}

▸ Functional Relations8 relations