X1204

3rd SARAGOSSA POINT OF X64

X1204 = reflection of X1092 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) { 1092, 3 }: Central Line L(1092, 3) { 3, 49 }: Central Line L(3, 49) { 4, 74 }: Central Line L(4, 74) { 25, 64 }: Central Line L(25, 64) { 378, 389 }: Central Line L(378, 389) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1092 = TRILINEAR CUBE OF X(3) (0.3503, 0.0118) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_4 = ORTHOCENTER (0.6122, 0.3958) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) 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_1204 = 3rd SARAGOSSA POINT OF X(64) (0.6497, 0.1923) A B C X1092 X3 X49 X4 X74 X25 X64 X378 X389 X1204 (a, b, c) = (5, 6, 7) | AB = 1

X1204 (3rd SARAGOSSA POINT OF X64) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1166)
Barycentrics: \(a^{2} (a^{2} - b^{2} - c^{2}) (a^{6} - 3 a^{2} (b^{2} - c^{2})^{2} + 2 (b^{2} - c^{2})^{2} (b^{2} + c^{2})) : :\)
Search Value (6, 9, 13): \(8.837658436441\)
▸ Incident Central Lines6 lines

{3, 49}, {4, 74}, {25, 64}, {217, 574}, {378, 389}, {578, 1199}

▸ Functional Relations6 relations