As illustrated, in a
right triangle ABC (AB = 3, BC = 4) the congruent
circles O_{1} and O_{2} are tangent to each other and to the
hypotenuse. AB is tangent to circle O_{1} and BC is tangent to
circle O_{2}. Find the measure of radius of circle O_{2}.

Background
of Problem 1193: Machu Picchu, "Lost City of the Incas".