X1809

INVERSE MIMOSA TRANSFORM OF X515

X1809 = isogonal conjugate of X1875
< 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, 8 }: Central Line L(3, 8) { 78, 255 }: Central Line L(78, 255) { 69, 1804 }: Central Line L(69, 1804) { 1259, 1265 }: Central Line L(1259, 1265) { 1295, 1309 }: Central Line L(1295, 1309) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1875 = ZOSMA TRANSFORM OF X(515) (0.6357, 0.6908) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1804 = INVERSE MIMOSA TRANSFORM OF X(223) (0.4495, 0.0488) X_1259 = ISOGONAL CONJUGATE OF X(1118) (0.3105, 0.0160) X_1265 = ISOTOMIC CONJUGATE OF X(1119) (0.2751, 0.0213) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_1309 = COLLINGS TRANSFORM OF X(860) (0.4052, -0.3994) X_1809 = INVERSE MIMOSA TRANSFORM OF X(515) (0.6320, -0.0327) A B C X1875 X3 X8 X78 X255 X69 X1804 X1259 X1265 X1295 X1309 X1809 (a, b, c) = (5, 6, 7) | AB = 1

X1809 (INVERSE MIMOSA TRANSFORM OF X515) 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 \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X515
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.581925364872\)
▸ Incident Central Lines5 lines

{3, 8}, {69, 1804}, {78, 255}, {1259, 1265}, {1295, 1309}

▸ Functional Relations1 relation