2021 April MIMC 10 Problems/Problem 23
On a coordinate plane, point denotes the origin which is the center of the diamond shape in the middle of the figure. Point
has coordinate
, and point
,
, and
are formed through
,
, and
rotation about the origin
, respectively. Quarter circle
(formed by the arc
and line segments
and
) has area
. Furthermore, another quarter circle
formed by arc
and line segments
,
is formed through a reflection of sector
across the line
. The small diamond centered at
is a square, and the area of the little square is
. Let
denote the area of the shaded region, and
denote the sum of the area of the regions
(formed by side
, arc
, and side
),
(formed by side
, arc
, and side
) and sectors
and
. Find
in the simplest radical form.
Solution
To be Released on April 26th.