Circle A has a center at #(1 ,3 )# and an area of #32 pi#. Circle B has a center at #(2 ,7 )# and an area of #28 pi#. Do the circles overlap?

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Answer 1 · 2016-12-16T11:38:01

#"Circles overlap."#

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#"the area of a Circle is given by formula :"area=pi*r^2#

#"let the radius of Circle A be " r_1;#

#"where r is the radius of Circle"#

#32cancel(pi)=cancel(pi)*r_1^2#

#r_1^2=32#

#r_1=sqrt(32)#

#r_1=5.66" "unit#

#"let the radius of Circle B be r_2"#

#28cancel(pi)=cancel(pi)*r_2^2#

#r_2^2=28#

#r_2=sqrt(28)#

#r_2=5.29" "unit#

#r_1+r_2=5.66+5.29#

#r_1+r_2=10.95" " unit#

#"now ; find "bar (O_1O_2)=d#

#d=sqrt((2-1)^2+(7-3)^2)#

#d=sqrt(1+16)#

#d=sqrt 17#

#d=4.12" "unit#

#"so d< "r_1+r_2#

#"circles overlap"#