X982

INTERSECTION OF LINES X1X_3 AND X2X_38

X982 = isogonal conjugate of X983
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 2, 38 }: Central Line L(2, 38) { 7, 256 }: Central Line L(7, 256) { 63, 238 }: Central Line L(63, 238) { 226, 262 }: Central Line L(226, 262) { 240, 278 }: Central Line L(240, 278) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2 = CENTROID (0.5374, 0.2000) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_7 = GERGONNE POINT (0.5903, 0.2769) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) A B C X983 X1 X3 X2 X38 X7 X256 X63 X238 X226 X262 X240 X278 X982 (a, b, c) = (5, 6, 7) | AB = 1

X982 (INTERSECTION OF LINES X1X_3 AND X2X_38) 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 \(f(a,b,c) = b^{2} - bc + c^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(2.280691626528\)
▸ Incident Central Lines17 lines

{1, 3}, {2, 38}, {7, 256}, {43, 518}, {58, 977}, {63, 238}, {72, 978}, {81, 985}, {222, 613}, {226, 262}, {240, 278}, {257, 330}, {310, 871}, {312, 726}, {404, 976}, {758, 995}, {846, 1001}

▸ Functional Relations5 relations