Two overlapping circles with equal radius form a shaded region as shown in the figure. Express the area of the region and the complete perimeter (combined arc length) in terms of r and the distance between center, #D#? Let #r=4 and D=6# and calculate?

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Answer 1 · 2016-10-29T05:18:54

see explanation.

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Given #AB=D=6, => AG=D/2=3#
Given #r=3#
#=> h=sqrt(r^2-(D/2)^2)=sqrt(16-9)=sqrt7#
#sinx =h/r=sqrt7/4#
#=> x=41.41^@#

Area GEF (red area) #=pir^2*(41.41/360)-1/2*3*sqrt7#
#=pi*4^2*(41.41/360)-1/2*3*sqrt7=1.8133#

Yellow Area # = 4 * #Red Area #= 4*1.8133=7.2532#

arc perimeter #(C->E->C)=4xx2pirxx(41.41/360)#
#= 4xx2pixx4xx(41.41/360)=11.5638#