X3355

REFLECTION OF X2131 IN X3

X3355 is the reflection of X2131 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) { 2131, 3 }: Central Line L(2131, 3) { 3, 2130 }: Central Line L(3, 2130) { 4, 3348 }: Central Line L(4, 3348) { 1, 3354 }: Central Line L(1, 3354) { 64, 3346 }: Central Line L(64, 3346) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3348 = ISOGONAL CONJUGATE OF X(3183) (0.4000, -0.1150) X_1 = INCENTER (0.5714, 0.2333) X_3354 = ISOGONAL CONJUGATE OF X(3353) (0.4568, 0.0283) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_3346 = ISOGONAL CONJUGATE OF X(1498) (0.4165, -0.8255) X_3355 = REFLECTION OF X(2131) IN X(3) (0.4675, 0.0474) A B C X2131 X3 X2130 X4 X3348 X1 X3354 X64 X3346 X3355 (a, b, c) = (5, 6, 7) | AB = 1

X3355 (REFLECTION OF X2131 IN X3) 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 \(f(a,b,c) = 2x_{3} - x_{2131} (using actual trilinear distances)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-169.876745382189\)

X3355 lies on the Darboux cubic.

▸ Incident Central Lines6 lines

{1, 3354}, {3, 2130}, {4, 3348}, {40, 3473}, {64, 3346}, {84, 3347}

▸ Functional Relations3 relations