Question

Circle A has a center at `(5 ,9 )` and an area of `65 pi`. Circle B has a center at `(7 ,2 )` and an area of `43 pi`. Do the circles overlap?

Answer 1

The circles overlap

Explanation:

Let radius of circle A as R1 and that of circle B as R2.
Area of circle A is `piR1^2=65pi`
`:.R1^2=65`
`R1=sqrt65`
Area of circle B is `piR2^2=43pi`
`:.R2^2=43`
`R2=sqrt43`
Let us find the Distance between the circle centres (5,9) and (7,2)
Distance D = `sqrt((5-7)^2+(9-2)^2)`
`=sqrt(-2^2+7^2)`
`=sqrt53`
`R1+R2=sqrt65+sqrt43>D=sqrt53`
Hence the circles overlap.