Home > Geometry > Distance between Points

Circle A has a center at #(8 ,-1 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #7 #. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Theodore Abad

No overlap. distance≈ 0.05

First step is to calculate the distance between the centres , using the #color(blue)" distance formula "#

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

where#(x_1,y_1) , (x_2,y_2) " are the coords of 2 points "#

let#(x_1,y_1) = (8,-1) " and " (x_2,y_2_) = (-2,-2)#

hence d#=sqrt((-2-8)^2+(-2+1)^2)=sqrt(101) ≈ 10.05#

now: radius of A + radius of B = 3+7 = 10

thus : 10 < 10.05 so no overlap and distance between them is

10.05 -10 = 0.05

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Claire Akin

The circles do overlap.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.