Question

Circle A has a center at `(2 ,3 )` and an area of `72 pi`. Circle B has a center at `(14 ,5 )` and an area of `48 pi`. Do the circles overlap?

Answer 1

Yes

Explanation:

The area of the first circle is`pi r^2=72pi`
`r=sqrt72`
`r=6sqrt2` =8.48 (2dp)
The area of the second circle is `pir^2= 48pi`
`r=sqrt48`
`r=4sqrt3`=6.93 (2dp)

The distance between the centres of the circles is found using Pythagoras.
The distance between the x coordinates is 12.
The distance between the y coordinates is 2
Draw the triangle . The length of the hypotenuse is `sqrt(12^2+2^2)`

=`sqrt148` =12.17(2dp)

If the circles did not overlap the the distance between their centres would have to be greater than the sum of the radii.
It is less so the circles overlap.