X(41) = X(6)-CEVA CONJUGATE OF X(31)

Trilinears

\(a2(b + c - a) : b2(c + a - b) : c2(a + b - c)\)

\(a2cot(A/2) : b2cot(B/2) : c2cot(C/2)\)

\(a2(a - s) : b2(b - s) : c2(c - s)\)

\(a tan A' : : , where A'B'C' is the excentral triangle\)

Barycentrics

\(a3(b + c - a) : b3(c + a - b) : c3(a + b - c)\)

Notes

For an artistic design generated by X(41), see X(244).

If you have The Geometer’s Sketchpad, you can view X(41).

X(41) lies on these lines: 1,101 3,218 6,48 9,21 25,42 31,32 37,584 55,220 58,609 65,910 219,1036 226,379 560,872 601,906 603,911 663,884

X(41) is the {X(32),:ref:X(213) <X(213)>}-harmonic conjugate of X(31). For a list of other harmonic conjugates of X(41), click Tables at the top of this page.

X(41) = isogonal conjugate of X(85)

X(41) = isotomic conjugate of X(20567)

X(41) = complement of X(21285)

X(41) = anticomplement of X(17046)

X(41) = X(i)-Ceva conjugate of X(j) for these (i,j): (6,31), (9,212), (284,55)

X(41) = crosspoint of X(i) and X(j) for these (i,j): (6,55), (9,33)

X(41) = crosssum of X(i) and X(j) for these (i,j): (1,169), (2,7), (57,77), (92,342), (226,1441), (514,1111)

X(41) = crossdifference of every pair of points on line X(522)X(693)

X(41) = X(i)-beth conjugate of X(j) for these (i,j): (41,32), (101,41), (220,220)

X(41) = X(75)-isoconjugate of X(57)

X(41) = X(92)-isoconjugate of X(77)

X(41) = trilinear product of vertices of 4th mixtilinear triangle

X(41) = trilinear product of vertices of 5th mixtilinear triangle

X(41) = trilinear product of PU(93)

X(41) = barycentric product of PU(104)

X(41) = PU(93)-harmonic conjugate of X(663)

X(41) = bicentric sum of PU(93)

X(41) = perspector of unary cofactor triangles of Gemini triangles 1 and 13