Question

Circle A has a center at `(3 ,2 )` and an area of `16 pi`. Circle B has a center at `(4 ,7 )` and an area of `80 pi`. Do the circles overlap?

Answer 1

`"circles overlap"`

Explanation:

`"What we have to do here is compare the distance (d)"`
`"between the centres to the sum of the radii"`

`• " if sum of radii">d" then circles overlap"`

`• " if sum of radii"< d" then no overlap"`

`"to calculate d use the "color(blue)"distance formula"`

`•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`"let "(x_1,y_1)=(3,2)" and "(x_2,y_2)=(4,7)`

`d=sqrt((4-3)^2+(7-2)^2)=sqrt(1+25)=sqrt26~~5.1`

`"to find the radii"`

`"circle A " to pir^2=16pirArrr^2=16rArrr=4`

`"circle B " to pir^2=80pirArrr^2=80rArrr=sqrt80=4sqrt5`

`"sum of radii "=4+4sqrt5~~12.94`

`"since sum of radii"> d" then circles overlap"`
graph{((x-3)^2+(y-2)^2-16)((x-4)^2+(y-7)^2-26)=0 [-10, 10, -5, 5]}