Circle A has a center at #(2 ,8 )# and a radius of #4 #. Circle B has a center at #(-3 ,3 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-04-04T01:57:57

Circles do not overlap. Smallest distance #d_b=5sqrt2-7=0.071067" "#unit

Compute the distance #d# between centers using distance formula

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((2--3)^2+(8-3)^2)#

#d=5sqrt2#

Add the measurements of the radii

#r_t=r_1+r_2=4+3=7#

Distance #d_b# between circles

#d_b=d-r_t=5sqrt2-7=0.071067" "#

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