X3212

X57-CEVA CONJUGATE OF X7

X3212 = isogonal conjugate of X2053
< 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) { 7, 8 }: Gergonne–Nagel Line { 2, 257 }: Central Line L(2, 257) { 57, 239 }: Central Line L(57, 239) { 279, 291 }: Central Line L(279, 291) { 607, 653 }: Central Line L(607, 653) { 1, 1447 }: Central Line L(1, 1447) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_2 = CENTROID (0.5374, 0.2000) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_1 = INCENTER (0.5714, 0.2333) X_1447 = -BETH CONJUGATE OF X(350) (1.1014, 1.0207) X_3212 = -CEVA CONJUGATE OF X(7) (0.6426, 0.3390) A B C X57 X7 X8 X2 X257 X239 X279 X291 X607 X653 X1 X1447 X3212 (a, b, c) = (5, 6, 7) | AB = 1

X3212 (X57-CEVA CONJUGATE OF X7) 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 \(f(a,b,c) = bc(bc - ab - ac)/(b + c - a)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.091594361095\)
▸ Incident Central Lines13 lines

{1, 1447}, {2, 257}, {7, 8}, {57, 239}, {241, 2275}, {273, 1829}, {279, 291}, {348, 1788}, {607, 653}, {672, 3177}, {1400, 2998}, {1431, 1966}, {1445, 2082}

▸ Functional Relations8 relations