X1934

TRILINEAR POLE OF PU(14)

X1934 = isogonal conjugate of X1933
< 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) { 257, 335 }: Central Line L(257, 335) { 38, 799 }: Central Line L(38, 799) { 75, 1581 }: Central Line L(75, 1581) { 561, 1109 }: Central Line L(561, 1109) { 334, 1441 }: Central Line L(334, 1441) { 764, 1244 }: Central Line L(764, 1244) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1933 = CROSSDIFFERENCE OF PU(14) (0.8524, 0.7964) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_1109 = TRILINEAR SQUARE OF X(523) (0.7246, 0.0705) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_1441 = -BETH CONJUGATE OF X(313) (0.5459, 0.2242) X_764 = TRILINEAR CUBE OF X(513) (1.2143, -0.1166) X_1244 = ISOGONAL CONJUGATE OF X(1009) (0.5903, 0.2249) X_1934 = TRILINEAR POLE OF PU(14) (1.0612, 0.0252) A B C X1933 X257 X335 X38 X799 X75 X1581 X561 X1109 X334 X1441 X764 X1244 X1934 (a, b, c) = (5, 6, 7) | AB = 1

X1934 (TRILINEAR POLE OF PU(14)) 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 \(f(a,b,c) = b^{2}c^{2}/(a^{4} - b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.476801531010\)
▸ Incident Central Lines7 lines

{38, 799}, {75, 1581}, {257, 335}, {334, 1441}, {561, 1109}, {764, 1244}, {1821, 1959}

▸ Functional Relations3 relations