X1940

CROSSSUM OF PU(16)

X1940 = X1937-Ceva conjugate of X243
< 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) { 4, 46 }: Central Line L(4, 46) { 29, 65 }: Central Line L(29, 65) { 34, 87 }: Central Line L(34, 87) { 56, 92 }: Central Line L(56, 92) { 3, 158 }: Central Line L(3, 158) { 201, 240 }: Central Line L(201, 240) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1937 = TRILINEAR POLE OF PU(15) (0.8541, -0.3793) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_1940 = CROSSSUM OF PU(16) (0.5801, 0.3721) A B C X1937 X243 X4 X46 X29 X65 X34 X87 X56 X92 X3 X158 X201 X240 X1940 (a, b, c) = (5, 6, 7) | AB = 1

X1940 (CROSSSUM OF PU(16)) 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 \(f(a,b,c) = \sec^{2} A + \sec B \sec C\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.131865808360\)
▸ Incident Central Lines23 lines

{1, 1075}, {2, 1118}, {3, 158}, {4, 46}, {20, 1857}, {27, 1882}, {29, 65}, {34, 87}, {35, 1784}, {55, 1895}, {56, 92}, {73, 1047}, {162, 1399}, {201, 240}, {225, 1247}, {281, 388}, {318, 1376}, {331, 1447}, {412, 1155}, {425, 1098}, {471, 580}, {1038, 1096}, {1816, 1896}

▸ Functional Relations6 relations