Question

Circle A has a center at `(1 ,8 )` and an area of `32 pi`. Circle B has a center at `(2 ,3 )` and an area of `28 pi`. Do the circles overlap?

Answer 1

The circles overlap.

Explanation:

Distance from the center of Circle A to center of Circle B:
`color(white)("XXX")d=sqrt((2-1)^2+(3-8)^2)`
`color(white)("XXXX")=sqrt(26)~~5.1`

Area of Circle (in general) `=pir^2`

`"Area"_A = pi*r_A^2 = 32pi`
`color(white)("XXX")r_A=sqrt(32)=4sqrt(2)~~5.7`

Since the radius of Circle A is greater than the distance between the centers of the two circles,
the center of Circle B is inside Circle A and the circles must overlap