Question

Circle A has a center at `(5 ,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

Yes they overlap

Explanation:

First circle
`(x-5)^2+(y-1)^2=r^2`

This is the general form of the equation of the circle
The area of the circle is `pir^2`which we are told equals`16pi`
So the radius of the first circle is 4
Like wise the area of the second circle is `sqrt67`

The distance between the centres of the 2 circles is
`sqrt((8-1)^2+(5-2)^2)`=`sqrt58`
This from Pythagoras.if you are not sure then draw the centre points on a graph and draw the right triangle.

If the circles did not overlap then the distance between the centres would be greater than the sum of the two radii. It is not.