X2154

X2-ISOCONJUGATE OF X16

X2154 = trilinear product of circumcircle intercepts of outer Napoleon circle
< 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, 14 }: Central Line L(10, 14) { 1, 1095 }: Central Line L(1, 1095) { 31, 2153 }: Central Line L(31, 2153) { 2152, 2173 }: Central Line L(2152, 2173) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2173 = -ISOCONJUGATE OF X(74) (1.2293, 2.5968) X_2153 = -ISOCONJUGATE OF X(15) (0.6114, 0.3163) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_1 = INCENTER (0.5714, 0.2333) X_1095 = TRILINEAR SQUARE OF X(16) (0.4127, 0.3906) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_2152 = -ISOCONJUGATE OF X(14) (1.1000, 1.3310) X_2154 = -ISOCONJUGATE OF X(16) (0.9495, -0.1417) A B C X2173 X2153 X10 X14 X1 X1095 X31 X2152 X2154 (a, b, c) = (5, 6, 7) | AB = 1

X2154 (X2-ISOCONJUGATE OF X16) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X16
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(6.522456837155\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A \csc(A - \pi /3)\)

▸ Incident Central Lines4 lines

{1, 1095}, {10, 14}, {31, 2153}, {2152, 2173}

▸ Functional Relations2 relations