Question

Circle A has a center at `(1 ,4 )` and an area of `28 pi`. Circle B has a center at `(7 ,9 )` and an area of `36 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

circles overlap

Explanation:

First step is to calculate the distance between the centres using the`color(blue)" distance formula "`
`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

where`(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "`

let `(x_1,y_1)=(1,4)" and " (x_2,y_2)=(7,9)`
hence `d = sqrt((7-1)^2 +(9-4)^2 )= sqrt(6^2+5^2)=sqrt61≈ 7.81`

Now require to find radii of circles,using A = `pir^2`

circle A : `pir^2 = 28pi rArr r^2= 28 rArr r = sqrt28`

circle B : `pir^2 = 36pi rArr r^2 = 36 rArrr = sqrt36 = 6`

radius of A + radius of B = `sqrt28 + 6 ≈ 11.292`

since the sum of the radii > distance between centres , the circles will overlap