X2665

TRILINEAR POLE OF PU(84)

X2665 = isogonal conjugate of X2664
< 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) { 6, 1045 }: Central Line L(6, 1045) { 1, 1655 }: Central Line L(1, 1655) { 43, 2279 }: Central Line L(43, 2279) { 292, 2238 }: Central Line L(292, 2238) { 190, 2663 }: Central Line L(190, 2663) { 1438, 1580 }: Central Line L(1438, 1580) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2664 = CROSSDIFFERENCE OF PU(84) (1.9947, 1.6278) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1045 = -CEVA CONJUGATE OF X(1) (0.6065, 0.2647) X_1 = INCENTER (0.5714, 0.2333) X_1655 = 2nd HATZIPOLAKIS PARALLELIAN POINT (0.5787, 0.2312) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_2279 = -ISOCONJUGATE OF X(1001) (0.6198, 0.3042) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_2238 = -ISOCONJUGATE OF X(741) (2.2505, 2.0410) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_2663 = CROSSSUM OF PU(84) (0.5786, 0.2418) X_1438 = -BETH CONJUGATE OF X(294) (0.9961, -0.1135) X_1580 = POINT ALUDRA (1.3094, 1.2033) X_2665 = TRILINEAR POLE OF PU(84) (1.0458, 0.0952) A B C X2664 X6 X1045 X1 X1655 X43 X2279 X292 X2238 X190 X2663 X1438 X1580 X2665 (a, b, c) = (5, 6, 7) | AB = 1

X2665 (TRILINEAR POLE OF PU(84)) 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 \(f(a,b,c) = 1/[bc(a + b)(a + c) - a^{2}(b + c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.979448329991\)
▸ Incident Central Lines6 lines

{1, 1655}, {6, 1045}, {43, 2279}, {190, 2663}, {292, 2238}, {1438, 1580}

▸ Functional Relations1 relation