X3460

X5-CEVA CONJUGATE OF X1

X3460 = isogonal conjugate of X3461
< 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, 54 }: Central Line L(1, 54) { 4, 484 }: Central Line L(4, 484) { 655, 1087 }: Central Line L(655, 1087) { 5, 2595 }: Central Line L(5, 2595) { 1726, 1745 }: Central Line L(1726, 1745) { 3336, 3459 }: Central Line L(3336, 3459) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1 = INCENTER (0.5714, 0.2333) X_54 = KOSNITA POINT (0.5880, 0.2176) X_4 = ORTHOCENTER (0.6122, 0.3958) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_655 = TRILINEAR POLE OF LINE X(1)X(5) (1.0449, 0.2400) X_1087 = TRILINEAR SQUARE OF X(5) (0.5422, 0.2643) X_2595 = CROSSSUM OF PU(68) (0.5650, 0.2411) X_1726 = MIMOSA TRANSFORM OF X(75) (0.5578, 0.3872) X_1745 = MIMOSA TRANSFORM OF X(255) (0.4689, -0.1747) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) X_3459 = ISOGONAL CONJUGATE OF X(195) (0.3786, 0.1244) X_3460 = -CEVA CONJUGATE OF X(1) (0.5384, 0.2645) A B C X5 X1 X54 X4 X484 X655 X1087 X2595 X1726 X1745 X3336 X3459 X3460 (a, b, c) = (5, 6, 7) | AB = 1

X3460 (X5-CEVA CONJUGATE OF X1) 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 \(f(a,b,c) = x(- x/u + y/v + z/w)\), where \(u : v : w\) = X5,\(x : y : z\) = X1
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(113.963125226931\)

X3460 lies on the Napoleon cubic.

▸ Incident Central Lines7 lines

{1, 54}, {3, 3469}, {4, 484}, {5, 2595}, {655, 1087}, {1726, 1745}, {3336, 3459}

▸ Functional Relations2 relations