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X(4), X(20), X(550)

X4-OAP points, see Table 53

infinite points of K003

other points below

K827 is the unique stelloid that passes through the X4-OAP points. Its radial center is X = X(14855).

It is spK(X3, Q) as in CL055 with Q = X(14641). The abscissa of Q in (X143, X389) is 7. See also the pencil mentioned in the page K071.

The reflection P of X(3) about Q lies on K827 and pK(X6, Q) meets (O) at the same points as K827.

K827 meets the line at infinity at the same points as K003. Their six remaining common points are A, B, C, H and two points Q1, Q2 on the line (L) = X(3)X(1495) and on the rectangular hyperbola (H) which is its isogonal transform.

K827 also contains the foci of the inscribed conic with center Q.