Question

Circle A has a center at `(6 ,5 )` and an area of `6 pi`. Circle B has a center at `(12 ,7 )` and an area of `36 pi`. Do the circles overlap?

Answer 1

Circles do overlap,

Explanation:

Distance between `(6,5)` and `(12,7)` is given by

`sqrt((12-6)^2+(7-5)^2)` i.e. `sqrt(6^2+2^2)` i.e. `sqrt40=6.3246`

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

radius of first circle is `sqrt6=2.4495` and

radius of second circle is `sqrt36=6`

As sum of the radius of the two circles at `8.4495` is more than distance of `6.3246` between them, circles do overlap,