X3182

X20-CEVA CONJUGATE OF X1

X3182 = X20-Ceva conjugate of X1
< 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) { 3345, 3 }: Central Line L(3345, 3) { 4, 57 }: Central Line L(4, 57) { 1, 64 }: Central Line L(1, 64) { 3, 223 }: Central Line L(3, 223) { 658, 1097 }: Central Line L(658, 1097) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3345 = ISOGONAL CONJUGATE OF X(1490) (0.4836, -5.5606) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_1097 = TRILINEAR SQUARE OF X(20) (0.3653, 0.0487) X_3182 = -CEVA CONJUGATE OF X(1) (0.5164, 5.7648) A B C X3345 X3 X4 X57 X1 X64 X223 X658 X1097 X3182 (a, b, c) = (5, 6, 7) | AB = 1

X3182 (X20-CEVA CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X20 and \(u : v : w\) = X1
Search Value (6, 9, 13): \(-1.988496855930\)

X3182 lies on the Darboux cubic.

▸ Incident Central Lines11 lines

{1, 64}, {3, 223}, {4, 57}, {20, 3347}, {40, 3346}, {579, 2270}, {658, 1097}, {1044, 1716}, {1490, 3348}, {1498, 3354}, {3183, 3473}

▸ Functional Relations5 relations