2013 UNCO Math Contest II Problems/Problem 3
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Problem
![[asy] filldraw(circle((0,-sqrt(2)/2),sqrt(2)/2),grey); filldraw(circle((0,0),1),white); draw((-sqrt(2)/2,-sqrt(2)/2)--(sqrt(2)/2,-sqrt(2)/2)--(0,0)--cycle,black); MP("C",(0,0),N);MP("A",(-sqrt(2)/2,-sqrt(2)/2),W);MP("B",(sqrt(2)/2,-sqrt(2)/2),E); [/asy]](http://latex.artofproblemsolving.com/6/f/4/6f454430810db95dc2f8781163526ce175e8850d.png)
Point 
is the center of a large circle that passes through both 
and
, and lies on the small circle whose diameter is 
. The area of the
small circle is 
. Find the area of the shaded 
, the region inside
the small circle and outside the large circle.
