X3454

ISOGONAL CONJUGATE OF X3453

X3454 is the isogonal conjugate of X3453.
< 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, 12 }: Central Line L(10, 12) { 2, 58 }: Central Line L(2, 58) { 5, 141 }: Central Line L(5, 141) { 118, 127 }: Central Line L(118, 127) { 121, 125 }: Central Line L(121, 125) { 34, 860 }: Central Line L(34, 860) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3453 = 1st SARAGOSSA POINT OF X(10) (0.6194, 0.3150) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2 = CENTROID (0.5374, 0.2000) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(92) (0.7856, 0.8494) X_3454 = ISOGONAL CONJUGATE OF X(3453) (0.5008, 0.1575) A B C X3453 X10 X12 X2 X58 X5 X141 X118 X127 X121 X125 X34 X860 X3454 (a, b, c) = (5, 6, 7) | AB = 1

X3454 (ISOGONAL CONJUGATE OF X3453) 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 \(f(a,b,c) = 1/(x(3453)\)
Search Value (6, 9, 13): \(3.568087066052\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = bc(b + c)[a(b^{2} + c^{2}) + b^{3} + c^{3}] (E\). Danneels)

▸ Incident Central Lines14 lines

{2, 58}, {5, 141}, {10, 12}, {34, 860}, {44, 1213}, {118, 127}, {121, 125}, {306, 2901}, {429, 1828}, {519, 1834}, {1046, 1698}, {1089, 1230}, {1104, 1125}, {1228, 1930}

▸ Functional Relations8 relations