2023 WSMO Team Round Problems/Problem 14
Problem
Consider quadrilateral with circumcircle centered at
. Given
, the circumcircle of
is tangent to the circumcircle of
. The circumcircle of
passes through the center of the circumcircle of
. Given the radius of the circumcircle of
is
. Denote
as the area and perimeter of
respectively, compute
. The answer can be expressed in the simplest form of
. Find