X1456

X516-BETH CONJUGATE OF X516

X1456 = X105-Ceva conjugate of X56
< 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) { 6, 19 }: Central Line L(6, 19) { 55, 223 }: Central Line L(55, 223) { 56, 269 }: Central Line L(56, 269) { 238, 241 }: Central Line L(238, 241) { 222, 354 }: Central Line L(222, 354) { 1, 971 }: Central Line L(1, 971) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_354 = WEILL POINT (0.5823, 0.2533) X_1 = INCENTER (0.5714, 0.2333) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_1456 = -BETH CONJUGATE OF X(516) (0.7238, 1.0576) A B C X516 X6 X19 X55 X223 X56 X269 X238 X241 X222 X354 X1 X971 X1456 (a, b, c) = (5, 6, 7) | AB = 1

X1456 (X516-BETH CONJUGATE OF X516) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X516
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.210020183361\)
▸ Incident Central Lines18 lines

{1, 971}, {6, 19}, {7, 1386}, {31, 1427}, {55, 223}, {56, 269}, {77, 1001}, {109, 1155}, {154, 1435}, {222, 354}, {227, 1253}, {238, 241}, {513, 663}, {518, 651}, {603, 1418}, {614, 1407}, {1042, 1104}, {1428, 1462}

▸ Functional Relations4 relations