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X(3), X(39), X(182), X(427)

X5-OAP points, see Table 53

infinite points of K102

points of pK(X6, P) on (O) where OP = – 1/4 OK

K823 is a cubic that passes through the four X5-OAP points. These points lie on the stelloid K665 and on a rectangular hyperbola (H) passing through X(140), X(550) and homothetic to the Jerabek hyperbola. See also K821, K822.

K823 meets the Grebe cubic K102 at three points on the line at infinity and six finite points on a circum-conic (H') passing through X(98).

K823 meets the circumcircle (O) at the same points as the isogonal pK with pivot P where OP = – 1/4 OK. SEARCH = 8.22972649397901.

K823 is tangent at X(3) to the Euler line.