X1172

1st SARAGOSSA POINT OF X48

X1172 = X27-Ceva conjugate of X28
< 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) { 4, 6 }: Van Aubel Line { 1, 19 }: Central Line L(1, 19) { 7, 27 }: Central Line L(7, 27) { 8, 29 }: Central Line L(8, 29) { 9, 33 }: Central Line L(9, 33) { 58, 84 }: Central Line L(58, 84) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1214 = ISOGONAL CONJUGATE OF X(1172) (0.5087, 0.1180) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1 = INCENTER (0.5714, 0.2333) X_19 = CLAWSON POINT (0.6246, 0.4244) X_7 = GERGONNE POINT (0.5903, 0.2769) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_8 = NAGEL POINT (0.4694, 0.1333) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_9 = MITTENPUNKT (0.5110, 0.1615) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) A B C X1214 X4 X6 X1 X19 X7 X27 X8 X29 X9 X33 X58 X84 X1172 (a, b, c) = (5, 6, 7) | AB = 1

X1172 (1st SARAGOSSA POINT OF X48) 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)
Search Value (6, 9, 13): \(6.368123769862\)

X1172 lies on the Feuerbach hyperbola.

▸ Incident Central Lines14 lines

{1, 19}, {4, 6}, {7, 27}, {8, 29}, {9, 33}, {21, 270}, {25, 941}, {37, 943}, {58, 84}, {104, 112}, {162, 1156}, {186, 1030}, {286, 648}, {406, 966}

▸ Functional Relations11 relations