Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(2 ,-1 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?

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Answer 1 · 2016-03-04T09:16:06

Yes, the circles overlap.

compute the center to center disance

Let #P_2(x_2, y_2)=(5, -2)# and #P_1(x_1, y_1)=(2, -1)#

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

#d=sqrt((5-2)^2+(-2--1)^2)#

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

#d=sqrt10=3.16#

Compute the sum of the radii

#r_t=r_1+r_2=3+2=5#

#r_1+r_2>d#

the circles overlap

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