X3512

ISOGONAL CONJUGATE OF X3509

X3512 is the isogonal conjugate of X3509.
< 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) { 335, 385 }: Central Line L(335, 385) { 55, 846 }: Central Line L(55, 846) { 19, 1423 }: Central Line L(19, 1423) { 6, 2114 }: Central Line L(6, 2114) { 1086, 2160 }: Central Line L(1086, 2160) { 1, 3506 }: Central Line L(1, 3506) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3509 = INTERSECTION OF LINES X(1)X(32) AND X(2)X(7) (5.8622, 7.9483) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2114 = POINT KEPLER V (0.1793, 0.8022) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_2160 = -ISOCONJUGATE OF X(35) (0.6185, 0.3356) X_1 = INCENTER (0.5714, 0.2333) X_3506 = INTERSECTION OF LINES X(2)X(98) AND X(32)X(694) (0.0474, 0.7964) X_3512 = ISOGONAL CONJUGATE OF X(3509) (0.9280, -0.1499) A B C X3509 X335 X385 X55 X846 X19 X1423 X6 X2114 X1086 X2160 X1 X3506 X3512 (a, b, c) = (5, 6, 7) | AB = 1

X3512 (ISOGONAL CONJUGATE OF X3509) 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 \(f(a,b,c) = 1/(a^{3} - b^{3} - c^{3} + abc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.285463337253\)

X3512 lies on the cubic Z(X385).

▸ Incident Central Lines9 lines

{1, 3506}, {6, 2114}, {19, 1423}, {55, 846}, {335, 385}, {511, 3507}, {1086, 2160}, {1654, 2893}, {3505, 3510}

▸ Functional Relations5 relations