Question

Circle A has a center at `(5 ,2 )` and an area of `15 pi`. Circle B has a center at `(4 ,7 )` and an area of `80 pi`. Do the circles overlap?

Answer 1

Circles do overlap.

Explanation:

Distance between `(5,2)` and `(4,7)` is given by

`sqrt((4-5)^2+(7-2)^2)` i.e. `sqrt((-1)^2+5^2)` i.e. `sqrt26=5.099`

As radius of a circle is given by `pir^2`,

radius of circle A is `sqrt15=3.873` and

radius of circle B is `sqrt80=8.944`

As sum of the radii of the two circles at `12.817` is more than distance between their centers which is `5.099`, circles do overlap,