X1252

ISOGONAL CONJUGATE OF X1086

X1252 is the isogonal conjugate of X1086.
< 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) { 59, 672 }: Central Line L(59, 672) { 100, 650 }: Central Line L(100, 650) { 101, 649 }: Central Line L(101, 649) { 44, 765 }: Central Line L(44, 765) { 110, 813 }: Central Line L(110, 813) { 644, 906 }: Central Line L(644, 906) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_906 = INTERSECTION OF LINES X(100)X(112) AND X(101)X(109) (-0.2109, 0.3287) X_1252 = ISOGONAL CONJUGATE OF X(1086) (0.4699, 0.3541) A B C X1086 X59 X672 X100 X650 X101 X649 X44 X765 X110 X813 X644 X906 X1252 (a, b, c) = (5, 6, 7) | AB = 1

X1252 (ISOGONAL CONJUGATE OF X1086) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1086
Search Value (6, 9, 13): \(0.782521288014\)
▸ Incident Central Lines9 lines

{44, 765}, {59, 672}, {100, 650}, {101, 649}, {110, 813}, {241, 1262}, {644, 906}, {902, 1110}, {1018, 1021}

▸ Functional Relations8 relations

Notes

X1252 is the vertex conjugate of the foci of the inellipse that is the barycentric square of the Nagel line. (Randy Hutson, October 15, 2018)