X₁₇₆₃

MIMOSA TRANSFORM OF X₃₂₆

X₁₇₆₃ = X₆₉-Ceva conjugate of X₁

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

X₁₇₆₃ (MIMOSA TRANSFORM OF X₃₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 25}, {6, 57}

• Related Centers: X₁ (INCENTER), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₆ (SYMMEDIAN POINT), X₅₇ (ISOGONAL CONJUGATE OF X₉)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X₃₂₆

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-14.418626275127\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin B)(\tan B) + (\sin C)(\tan C) - (\sin A)(\tan A)\) (Randy Hutson, 9/23/2011)

▸ Incident Central Lines12 lines

{1, 25}, {2, 169}, {6, 57}, {9, 440}, {19, 226}, {40, 64}, {43, 46}, {63, 573}, {73, 1452}, {198, 1214}, {329, 1766}, {1711, 1756}

▸ Functional Relations6 relations

• X₁₇₆₃ = isogonal conjugate of X₇₀₉₇

• X₁₇₆₃ = isotomic conjugate of polar conjugate of X₃₆₁₀₃

• X₁₇₆₃ = anticomplement of X₃₆₈₅₀

• X₁₇₆₃ = crossdifference of every pair of points on line X₂₅₂₂X₃₉₀₀

• X₁₇₆₃ = X₆₉-Ceva conjugate of X₁

• X₁₇₆₃ = X_i-aleph conjugate of X_j for these (i,j): (1, 1716), (2, 46), (63, 1745), (69, 1763), (75, 1726), (174, 1722), (188, 1721), (366, 1707), (508, 1723), (556, 1158), (664, 1020)