X₁₇₄₉

MIMOSA TRANSFORM OF X₂₆₅

X₁₇₄₉ = midpoint of X₄₈₄ and X₃₀₆₅

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₇₄₉ (MIMOSA TRANSFORM OF X₂₆₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {484, 3065}

• Related Centers: X₄₈₄ (1st EVANS PERSPECTOR), X₃₀₆₅ (ISOGONAL CONJUGATE OF X₄₈₄)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X₂₆₅

Barycentrics: \(a (a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} - 3 a^{4} c^{2} - a^{2} b^{2} c^{2} + b^{4} c^{2} + 3 a^{2} c^{4} + b^{2} c^{4} - c^{6}) : :\)

Search Value (6, 9, 13): \(-0.800763073132\)

▸ Alternate Coordinates1 form

• Trilinears: \(a^{6} - 3 a^{4} (b^{2} + c^{2}) + a^{2} (3 b^{4} - b^{2} c^{2} + 3 c^{4}) - (b^{2} - c^{2})^{2} (b^{2} + c^{2}) : :\)

▸ Linear Combinations1 combination

• X₁₇₄₉ = \((2r + R)\) X₁ - \(4 r\) X₂₁

▸ Incident Central Lines57 lines

{1, 21}, {2, 16763}, {3, 16767}, {5, 79}, {30, 80}, {35, 17637}, {36, 2771}, {46, 7701}, {56, 13465}, {65, 22936}, {90, 18514}, {442, 12623}, {499, 14450}, {1087, 2962}, {1733, 16568}, {1755, 16546}, {1768, 5131}, {1776, 3583}, {1858, 14794}, {2099, 28453}, {2475, 18395}, {3086, 31888}, {3218, 3582}, {3219, 3584}, {3337, 3649}, {3375, 3376}, {3383, 3384}, {3585, 7098}, {3648, 5046}, {3820, 16152}, {3929, 17699}, {5427, 6265}, {5441, 10950}, {5444, 31650}, {5445, 5499}, {5692, 19525}, {5694, 14804}, {5844, 10543}, {5902, 7489}, {5903, 13743}, {6701, 7504}, {6949, 16116}, {7161, 13995}, {7280, 16132}, {7308, 17700}, {7491, 16113}, {7741, 16159}, {10266, 23016}, {10573, 15680}, {11263, 27003}, {12535, 13129}, {14526, 18244}, {14527, 17768}, {15079, 16150}, {15950, 16140}, {16155, 26475}, {17757, 18253}

▸ Functional Relations10 relations

• X₁₇₄₉ = midpoint of X₄₈₄ and X₃₀₆₅

• X₁₇₄₉ = reflection of X_i in X_j for these {i,j}: {3649, 15325}, {17757, 18253}

• X₁₇₄₉ = X₂₁₆₆-Ceva conjugate of X₁

• X₁₇₄₉ = crosspoint of X₂₄₀₄₁ and X₃₂₆₈₀

• X₁₇₄₉ = crosssum of X₂₆₂₄ and X₂₆₄₃

• X₁₇₄₉ = crossdifference of every pair of points on line {661, 17438}

• X₁₇₄₉ = barycentric product X_i*X_j for these {i,j}: {75, 11063}, {311, 19306}, {799, 6140}, {1157, 14213}, {2349, 10272}, {3470, 14206}, {8562, 32680}, {10413, 24041}

• X₁₇₄₉ = X_i-isoconjugate of X_j for these (i,j): {2, 14579}, {6, 13582}, {54, 1263}, {74, 3471}, {186, 15392}, {323, 11071}, {523, 1291}, {3459, 14367}, {15109, 30526}

• X₁₇₄₉ = barycentric quotient X_i/X_j for these {i,j}: {{1, 13582}, {31, 14579}, {163, 1291}, {1157, 2167}, {1953, 1263}, {2173, 3471}, {3470, 2349}, {6140, 661}, {8562, 32679}, {10272, 14206}, {10413, 1109}, {11063, 1}, {19306, 54}}

• X₁₇₄₉ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {21, 11684, 3878}, {46, 7701, 16118}, {191, 6763, 11684}, {896, 1725, 6149}, {1725, 6149, 1}, {1755, 16562, 16546}, {1822, 1823, 2964}, {3336, 3467, 5}, {3649, 10021, 5443}, {5441, 16139, 11010}, {16139, 16141, 5441}, {17637, 22937, 35}