Home > Geometry > Distance between Points

Circle A has a center at #(5 ,4 )# and a radius of #9 #. Circle B has a center at #(1 ,-2 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Circles do overlap.

Distance between center of Circle A at #(5,4)# and center of Circle Bat #(1,-2)# is given by

#sqrt((5-1)^2+(4-(-2))^2)# i.e. #sqrt(4^2+6^2)# i.e. #sqrt52=7.2111#

As sum of the radii of the two circles at #15# is more than distance between their centers which is #7.2111#, circles do overlap,

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

Answer 2

Savannah Aguilar

To determine if the circles overlap, we need to calculate the distance between their centers and compare it to the sum of their radii. If the distance between the centers is less than the sum of the radii, then the circles overlap. Otherwise, they do not overlap, and the smallest distance between them is the difference between the distance between their centers and the sum of their radii.

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.