Malfatti's Tangent Triangle Problem
Draw within a given Triangle three Circles, each of which is Tangent to theother two and to two sides of the Triangle. Denote the three Circles so constructed 
, 
, and
. Then is tangent to 
and 
, is tangent to 
and 
, and is tangentto and .
References
Dörrie, H. ``Malfatti's Problem.'' §30 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 147-151, 1965. Forder, H. G. Higher Course Geometry. Cambridge, England: Cambridge University Press, pp. 244-245, 1931. Fukagawa, H. and Pedoe, D. Japanese Temple Geometry Problems (San Gaku). Winnipeg: The Charles Babbage Research Centre, pp. 106-120, 1989. Gardner, M. Fractal Music, Hypercards, and More Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 163-165, 1992. Goldberg, M. ``On the Original Malfatti Problem.'' Math. Mag. 40, 241-247, 1967. Lob, H. and Richmond, H. W. ``On the Solution of Malfatti's Problem for a Triangle.'' Proc. London Math. Soc. 2, 287-304, 1930. Woods, F. S. Higher Geometry. New York: Dover, pp. 206-209, 1961.
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