X1729

MIMOSA TRANSFORM OF X85

X1729 = X331-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) { 5, 9 }: Central Line L(5, 9) { 63, 169 }: Central Line L(63, 169) { 19, 1158 }: Central Line L(19, 1158) { 57, 1375 }: Central Line L(57, 1375) { 607, 1735 }: Central Line L(607, 1735) { 920, 1752 }: Central Line L(920, 1752) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_331 = ISOTOMIC CONJUGATE OF X(219) (0.6062, 0.4046) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_9 = MITTENPUNKT (0.5110, 0.1615) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1158 = CIRCUMCENTER OF EXTOUCH TRIANGLE (0.5179, 0.3262) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1375 = EVANS POINT (0.9628, 1.3129) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_1735 = MIMOSA TRANSFORM OF X(102) (0.8922, 0.8226) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) X_1752 = MIMOSA TRANSFORM OF X(277) (0.4388, 0.3416) X_1729 = MIMOSA TRANSFORM OF X(85) (0.6667, 0.4631) A B C X331 X1 X5 X9 X63 X169 X19 X1158 X57 X1375 X607 X1735 X920 X1752 X1729 (a, b, c) = (5, 6, 7) | AB = 1

X1729 (MIMOSA TRANSFORM OF X85) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X85, arycentrics \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.148625510014\)
▸ Incident Central Lines7 lines

{5, 9}, {19, 1158}, {57, 1375}, {63, 169}, {607, 1735}, {920, 1752}, {1723, 1744}

▸ Functional Relations2 relations