The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_179 called the first Ajima-Malfatti point (Kimberling and MacDonald 1990, Kimberling 1994). This point has triangle center function α_179 = sec^4(1/4 A). Similarly, letting A'', B'', and C'' be the excenters of Δ A B C, then the lines A' A'', B' B'', and C' C'' are coincident in another point called the second Ajima-Malfatti point, which is Kimberling center X_180 (but is at present given erroneously in Kimberling's tabulation). These points are sometimes simply called the Malfatti points.
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