X1196

3rd SARAGOSSA POINT OF X25

X1196 = complement of X305
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 305 }: Central Line L(2, 305) { 2, 39 }: Central Line L(2, 39) { 25, 32 }: Central Line L(25, 32) { 22, 187 }: Central Line L(22, 187) { 111, 251 }: Central Line L(111, 251) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_22 = EXETER POINT (0.4143, -0.1221) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_111 = PARRY POINT (0.9885, -0.0457) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_1196 = 3rd SARAGOSSA POINT OF X(25) (0.6432, 0.2801) A B C Ma Mb Mc X2 X305 X39 X25 X32 X22 X187 X111 X251 X1196 (a, b, c) = (5, 6, 7) | AB = 1

X1196 (3rd SARAGOSSA POINT OF X25) 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 \(f(a,b,c) = a(b^{4} + c^{4} + a^{2}b^{2} + a^{2}c^{2} - 2b^{2}c^{2})\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.673062670697\)
▸ Incident Central Lines31 lines

{2, 39}, {3, 1611}, {6, 2056}, {22, 187}, {23, 1627}, {25, 32}, {51, 3051}, {111, 251}, {115, 427}, {184, 1692}, {216, 230}, {232, 800}, {233, 3815}, {394, 5028}, {511, 1613}, {612, 1500}, {614, 1015}, {682, 3080}, {1084, 2493}, {1368, 5254}, {1495, 1501}, {1570, 1993}, {1915, 3506}, {1995, 5007}, {2092, 5275}, {2275, 5272}, {2276, 5268}, {2670, 4263}, {3094, 3819}, {3231, 3917}, {3796, 5033}

▸ Functional Relations6 relations