  More than two centuries ago Malfatti (see \cite{malfatti}) raised and solved
the following problem (the so-called Malfatti's construction problem):Construct
three circles into a triangle so that each of them touches the two others from
outside moreover touches two sides of the triangle too. It is an interesting
fact that nobody investigated this problem on the hyperbolic plane, while the
case of the sphere was solved simultaneously with the Euclidean case. In order
to compensate this shortage we solve the following exercise: {\em Determine
three cycles of the hyperbolic plane so that each of them touches the two
others moreover touches two of three given cycles of the hyperbolic plane.}

Metric Geometry