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Ajima-Malfatti Points

 
   
Ajima-MalfattiPoints

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

 alpha_(179)=sec^4(1/4A).
Ajima-MalfattiPoint2

Similarly, letting A^(''), B^(''), and C^('') be the excenters of DeltaABC, 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 (Kimberling 1994).


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