X2786

ISOGONAL CONJUGATE OF X2702

X2786 is the isogonal conjugate of X2702.
< 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) { 99, 101 }: Central Line L(99, 101) { 98, 103 }: Central Line L(98, 103) { 115, 116 }: Central Line L(115, 116) { 114, 118 }: Central Line L(114, 118) { 148, 150 }: Central Line L(148, 150) { 147, 152 }: Central Line L(147, 152) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2702 = SR(X(98), X(103)) (1.0071, 0.0449) X_99 = STEINER POINT (0.1109, 0.4322) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_98 = TARRY POINT (0.8891, -0.2281) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_2786 = ISOGONAL CONJUGATE OF X(2702) (0.9745, 0.5916) A B C X2702 X99 X101 X98 X103 X115 X116 X114 X118 X148 X150 X147 X152 X2786 (a, b, c) = (5, 6, 7) | AB = 1

X2786 (ISOGONAL CONJUGATE OF X2702) 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 \(f(a,b,c) = bc(b - c)(b^{2} + c^{2} - a^{2} + bc- ab - ac)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines8 lines

{30, 511}, {98, 103}, {99, 101}, {114, 118}, {115, 116}, {147, 152}, {148, 150}, {671, 903}

▸ Functional Relations6 relations