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X(1), X(4), X(80), X(517), X(2716)

K684 is a Fuhrmann-Feuerbach cubic, see details at K681 and also K529, K682, K683, K685.

Its singular focus is X(355), the center of the Fuhrmann circle.The line OI = X(1)X(3) is the real asymptote and the line X(5)X(10) is the orthic line.