X3472

X20-CEVA CONJUGATE OF X3345

X3472 = reflection of X3354 in X3
< 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) { 3354, 3 }: Central Line L(3354, 3) { 40, 2131 }: Central Line L(40, 2131) { 1, 3348 }: Central Line L(1, 3348) { 4, 3347 }: Central Line L(4, 3347) { 64, 3345 }: Central Line L(64, 3345) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3354 = ISOGONAL CONJUGATE OF X(3353) (0.4568, 0.0283) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_40 = BEVAN POINT (0.4286, -0.0292) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_1 = INCENTER (0.5714, 0.2333) X_3348 = ISOGONAL CONJUGATE OF X(3183) (0.4000, -0.1150) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3347 = ISOGONAL CONJUGATE OF X(3182) (0.3848, -0.3283) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_3345 = ISOGONAL CONJUGATE OF X(1490) (0.4836, -5.5606) X_3472 = -CEVA CONJUGATE OF X(3345) (0.5432, 0.1758) A B C X3354 X3 X40 X2131 X1 X3348 X4 X3347 X64 X3345 X3472 (a, b, c) = (5, 6, 7) | AB = 1

X3472 (X20-CEVA CONJUGATE OF X3345) 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 \(u : v : w\) = X20,\(x : y : z\) = X3345
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(25.787787339447\)

X3472 lies on the Darboux cubic.

▸ Incident Central Lines7 lines

{1, 3348}, {3, 3354}, {4, 3347}, {20, 3473}, {40, 2131}, {64, 3345}, {84, 3346}

▸ Functional Relations3 relations