Question

Circle A has a center at `(2 ,9 )` and an area of `16 pi`. Circle B has a center at `(3 ,8 )` and an area of `67 pi`. Do the circles overlap?

Answer 1

Circles do overlap

Explanation:

Distance between `(2,9)` and `(3,8)` is given by

`sqrt((3-2)^2+(8-9)^2)` i.e. `sqrt(1+1)` i.e. `sqrt2=1.4142`

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

radius of circle A is `sqrt16=4` and

radius of second circle is `sqrt67=8.1854`

As sum of the radii of the two circles at `12.1854` is more than distance of `1.4142` between them, circles do overlap,