+0

i would put a title but im too confused

+1
369
2
+303

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.

Feb 20, 2021

#1
0

The area of the gray region is 26*pi.

Feb 20, 2021
#2
+1486
+2

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

Feb 21, 2021