X949

ISOGONAL CONJUGATE OF X948

X949 is the isogonal conjugate of X948.
< 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) { 3, 41 }: Central Line L(3, 41) { 6, 77 }: Central Line L(6, 77) { 2, 294 }: Central Line L(2, 294) { 78, 220 }: Central Line L(78, 220) { 1, 607 }: Central Line L(1, 607) { 48, 1037 }: Central Line L(48, 1037) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_948 = INTERSECTION OF LINES X(1)X(4) AND X(6)X(7) (0.5840, 0.2831) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_2 = CENTROID (0.5374, 0.2000) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_1 = INCENTER (0.5714, 0.2333) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_949 = ISOGONAL CONJUGATE OF X(948) (0.5571, 0.1869) A B C X948 X3 X41 X6 X77 X2 X294 X78 X220 X1 X607 X48 X1037 X949 (a, b, c) = (5, 6, 7) | AB = 1

X949 (ISOGONAL CONJUGATE OF X948) 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 \(f(a,b,c) = au/[a^{3} - a^{2}(b + c) + a(b + c)^{2} - (b - c)(b^{2} - c^{2})]\), where \(u : v : w\) = X9
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): \(2.379115196684\)
▸ Incident Central Lines6 lines

{1, 607}, {2, 294}, {3, 41}, {6, 77}, {48, 1037}, {78, 220}

▸ Functional Relations2 relations