Two circles share a common chord $\overline{PQ}.$ The chord cuts off a $90^\circ$ arc of circle $A$ and a $60^\circ$ arc of circle $B$. If the area of quadrilateral $APBQ$ is $6+6\sqrt 3.$ Find the combined area of the gray regions.
The area of the gray region is 26*pi.
PQ / 2 ==> x
x*( x + x / tan30º ) = 6 + 6√3 x = 2.449491
Radius AP = x / sin45º = 2√3
Radius BP = x / sin30º = 4.898979486
Area = [AP2*pi (270/360)] + [BP2*pi (300/360)]
Area = 29pi
+308 
