Question

Circle A has a center at `(2 ,1 )` and an area of `16 pi`. Circle B has a center at `(2 ,8 )` and an area of `67 pi`. Do the circles overlap?

Answer 1

Circles do overlap

Explanation:

Distance between `(2,1)` and `(2,8)` is `8-1)=7` as `x` coordinates are common.

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

radius of circle A is `sqrt16=4` and

radius of circle B is `sqrt67=8.1854`

As sum of the radius of the two circles at `12.1854` is more than distance of `7` between them, circles do overlap,