X1722

MIMOSA TRANSFORM OF X56

X1722 = {X8947,X8949}-harmonic conjugate of X1721
< 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) { 1, 2 }: Nagel Line { 40, 238 }: Central Line L(40, 238) { 9, 986 }: Central Line L(9, 986) { 87, 937 }: Central Line L(87, 937) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1721 = MIMOSA TRANSFORM OF X(55) (0.6494, 0.4136) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_40 = BEVAN POINT (0.4286, -0.0292) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_9 = MITTENPUNKT (0.5110, 0.1615) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_937 = ISOGONAL CONJUGATE OF X(936) (0.6143, 0.2920) X_1722 = MIMOSA TRANSFORM OF X(56) (0.8571, 0.5132) A B C X1721 X1 X2 X40 X238 X9 X986 X87 X937 X1722 (a, b, c) = (5, 6, 7) | AB = 1

X1722 (MIMOSA TRANSFORM OF X56) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X56
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.616816835133\)
▸ Incident Central Lines21 lines

{1, 2}, {4, 1716}, {9, 986}, {34, 1788}, {40, 238}, {46, 1707}, {57, 1773}, {87, 937}, {169, 1046}, {171, 1453}, {223, 1047}, {269, 979}, {427, 1039}, {429, 1717}, {920, 1772}, {958, 988}, {1040, 1837}, {1104, 1376}, {1254, 1445}, {1711, 1720}, {1723, 1880}

▸ Functional Relations3 relations