Question

Circle A has a center at `(8 ,7 )` and an area of `81 pi`. Circle B has a center at `(4 ,3 )` and an area of `36 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

Circles do overlap.

Explanation:

Distance between `(8,7)` and `(4,3)` is given by

`sqrt((8-4)^2+(7-3)^2)` i.e. `sqrt(4^2+4^2)` i.e. `sqrt32=5.6569`

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

radius of circle A is `sqrt81=9` and

radius of second circle is `sqrt16=4`

As sum of the radii of the two circles at `13` is more than distance between their centers which is `5.6569`, circles do overlap,