X2956

EXCENTRAL-ISOGONAL CONJUGATE OF X84

X2956 is the excentral-isogonal conjugate of X84.
< 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, 1394 }: Central Line L(1, 1394) { 1, 84 }: Central Line L(1, 84) { 266, 505 }: Central Line L(266, 505) { 223, 1158 }: Central Line L(223, 1158) { 109, 1490 }: Central Line L(109, 1490) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_1394 = -BETH CONJUGATE OF X(20) (0.4977, -0.6923) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_266 = ISOGONAL CONJUGATE OF X(188) (0.6074, 0.2891) X_505 = 3rd ISOSCELIZER POINT (0.6161, 0.3801) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_1158 = CIRCUMCENTER OF EXTOUCH TRIANGLE (0.5179, 0.3262) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1490 = ∩X(3)X(9) (0.3929, -0.4775) X_2956 = EXCENTRAL-ISOGONAL CONJUGATE OF X(84) (0.4240, -1.6179) A B C X1 X1394 X84 X266 X505 X223 X1158 X109 X1490 X2956 (a, b, c) = (5, 6, 7) | AB = 1

X2956 (EXCENTRAL-ISOGONAL CONJUGATE OF X84) 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) is as described just before X2883
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.206612130556\)
▸ Incident Central Lines11 lines

{1, 84}, {46, 1743}, {109, 1490}, {165, 1745}, {223, 1158}, {266, 505}, {651, 1103}, {978, 1044}, {1046, 1719}, {1249, 1838}, {1750, 1771}

▸ Functional Relations3 relations