X3461

ISOGONAL CONJUGATE OF X3460

X3461 is the isogonal conjugate of X3460.
< 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, 2120 }: Central Line L(1, 2120) { 5, 2595 }: Central Line L(5, 2595) { 195, 3468 }: Central Line L(195, 3468) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_1 = INCENTER (0.5714, 0.2333) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_2595 = CROSSSUM OF PU(68) (0.5650, 0.2411) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_3468 = -CEVA CONJUGATE OF X(3336) (0.5161, 0.0130) X_3461 = ISOGONAL CONJUGATE OF X(3460) (0.6102, 0.2013) A B C X54 X1 X2120 X5 X2595 X195 X3468 X3461 (a, b, c) = (5, 6, 7) | AB = 1

X3461 (ISOGONAL CONJUGATE OF X3460) 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 \(f(a,b,c) = 1/x(3460)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.327534577045\)

X3461 lies on the Napoleon cubic.

▸ Incident Central Lines3 lines

{1, 2120}, {5, 2595}, {195, 3468}

▸ Functional Relations2 relations