X1755

MIMOSA TRANSFORM OF X287

X1755 = X6-isoconjugate of X290
< 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) { 19, 27 }: Central Line L(19, 27) { 31, 48 }: Central Line L(31, 48) { 44, 513 }: Central Line L(44, 513) { 6, 893 }: Central Line L(6, 893) { 610, 1707 }: Central Line L(610, 1707) { 1580, 1581 }: Central Line L(1580, 1581) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1821 = ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X(287) (0.8340, -0.1768) X_19 = CLAWSON POINT (0.6246, 0.4244) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_1707 = MIMOSA TRANSFORM OF X(6) (0.7574, 0.4777) X_1580 = POINT ALUDRA (1.3094, 1.2033) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_1755 = MIMOSA TRANSFORM OF X(287) (1.5943, 2.3982) A B C X1821 X19 X27 X31 X48 X44 X513 X6 X893 X610 X1707 X1580 X1581 X1755 (a, b, c) = (5, 6, 7) | AB = 1

X1755 (MIMOSA TRANSFORM OF X287) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X287
Barycentrics: \(a^{2} (a^{2} \cos B \cos C - b c \cos^{2} A) : :\)
Search Value (6, 9, 13): \(-4.092117385536\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(a \cos(A + \omega ) : :\)

  • Trilinears: \((\cot A + \cot B + \cot C) \tan A - (\tan A + \tan B + \tan C) \cot A : :\)

  • Trilinears: \(a^{2} (a^{2} b^{2} + a^{2} c^{2} - b^{4} - c^{4}) : :\)

▸ Incident Central Lines6 lines

{6, 893}, {19, 27}, {31, 48}, {44, 513}, {610, 1707}, {1580, 1581}

▸ Functional Relations10 relations