2023 WSMO Accuracy Round Problems/Problem 9
Problem
Given circles with radius
respectively, they are externally tangent to each other. The diameters of
,
are
respectively, satisfying
and
is an external tangent of the circles. The third circle
passes through
and is tangent to
. If the minimum possible value of the radius of
is
, where
is positive, and
is squarefree, find