X1910

TRILINEAR POLE OF PU(23)

X1910 = X1821-Ceva conjugate of X293
< 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) { 10, 98 }: Central Line L(10, 98) { 48, 75 }: Central Line L(48, 75) { 1, 163 }: Central Line L(1, 163) { 65, 172 }: Central Line L(65, 172) { 19, 560 }: Central Line L(19, 560) { 37, 692 }: Central Line L(37, 692) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1821 = ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X(287) (0.8340, -0.1768) X_293 = ISOGONAL CONJUGATE OF X(240) (0.7839, -0.0636) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_98 = TARRY POINT (0.8891, -0.2281) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1 = INCENTER (0.5714, 0.2333) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_19 = CLAWSON POINT (0.6246, 0.4244) X_560 = 4th POWER POINT (0.6520, 0.3639) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_1910 = TRILINEAR POLE OF PU(23) (0.9516, -0.2978) A B C X1821 X293 X10 X98 X48 X75 X1 X163 X65 X172 X19 X560 X37 X692 X1910 (a, b, c) = (5, 6, 7) | AB = 1

X1910 (TRILINEAR POLE OF PU(23)) 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 \(f(a,b,c) = a/(a^{2}\cos B \cos C - bc \cos^{2} A)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-9.947684777762\)
▸ Incident Central Lines7 lines

{1, 163}, {10, 98}, {19, 560}, {37, 692}, {48, 75}, {65, 172}, {1580, 1581}

▸ Functional Relations5 relations