Y by HamstPan38825, Adventure10, Mango247
Let
be an isosceles trapezoid with
,
, and
. Denote by
and
the incircles of
and
respectively. Suppose that both
and
have radii of length
. The square of the distance between the centers of the two circles can be written in the form
, where
,
, and
are positive integers such that
is not divisible by the square of any prime. What is
?

















