X2306

X2-ISOCONJUGATE OF X1250

X2306 = X1081-Ceva conjugate of X1251
< 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) { 1, 15 }: Central Line L(1, 15) { 13, 79 }: Central Line L(13, 79) { 2, 1081 }: Central Line L(2, 1081) { 6, 1406 }: Central Line L(6, 1406) { 65, 2153 }: Central Line L(65, 2153) { 1082, 1255 }: Central Line L(1082, 1255) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1081 = POINT ALPHECCA (0.6056, 0.3226) X_1251 = ISOGONAL CONJUGATE OF X(1082) (0.5908, 0.2784) X_1 = INCENTER (0.5714, 0.2333) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1406 = -BETH CONJUGATE OF X(46) (0.6653, 0.5088) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_2153 = -ISOCONJUGATE OF X(15) (0.6114, 0.3163) X_1082 = POINT ALPHERATZ (0.5483, 0.1908) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5639, 0.2247) X_2306 = -ISOCONJUGATE OF X(1250) (0.6238, 0.3555) A B C X1081 X1251 X1 X15 X13 X79 X2 X6 X1406 X65 X2153 X1082 X1255 X2306 (a, b, c) = (5, 6, 7) | AB = 1

X2306 (X2-ISOCONJUGATE OF X1250) 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 X1250
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(0.012420080814\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A \sec(A/2) \sec(A + \pi /6)\)

▸ Incident Central Lines6 lines

{1, 15}, {2, 1081}, {6, 1406}, {13, 79}, {65, 2153}, {1082, 1255}

▸ Functional Relations1 relation