2015 AIME II Problems/Problem 15
Problem
Circles and
have radii
and
, respectively, and are externally tangent at point
. Point
is on
and point
is on
such that
is a common external tangent of the two circles. A line
through
intersects
again at
and intersects
again at
. Points
and
lie on the same side of
, and the areas of
and
are equal. This common area is
, where
and
are relatively prime positive integers. Find
.