X3357

MIDPOINT OF X3 AND X64

X3357 is the midpoint of X3 and X64.
< 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) { 3, 64 }: Central Line L(3, 64) { 4, 74 }: Central Line L(4, 74) { 185, 378 }: Central Line L(185, 378) { 389, 1593 }: Central Line L(389, 1593) { 550, 1503 }: Central Line L(550, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_4 = ORTHOCENTER (0.6122, 0.3958) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_389 = CENTER OF THE TAYLOR CIRCLE (0.6078, 0.2800) X_1593 = POINT CEBALRAI (0.5972, 0.3563) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_1503 = POINT ARKAB (0.4818, -0.3843) X_3357 = MIDPOINT OF X(3) AND X(64) (0.5289, 0.8482) A B C X3 X64 X4 X74 X185 X378 X389 X1593 X550 X1503 X3357 (a, b, c) = (5, 6, 7) | AB = 1

X3357 (MIDPOINT OF X3 AND X64) 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 \(f(a,b,c) = x_{3} + x_{64} (using actual trilinear distances)\)
Barycentrics: \(a^{2} (a^{8} - a^{6} (b^{2} + c^{2}) - a^{4} (3 b^{4} - 8 b^{2} c^{2} + 3 c^{4}) + 5 a^{2} (b^{2} - c^{2})^{2} (b^{2} + c^{2}) - 2 (b^{2} - c^{2})^{2} (b^{4} + 3 b^{2} c^{2} + c^{4})) : :\)
Search Value (6, 9, 13): \(19.204843480118\)
▸ Linear Combinations1 combination
▸ Incident Central Lines11 lines

{4, 74}, {20, 2888}, {140, 2883}, {185, 378}, {195, 2935}, {382, 1853}, {389, 1593}, {550, 1503}, {576, 2781}, {1092, 2071}, {1192, 1598}

▸ Functional Relations6 relations