Question

Circle A has a center at `(5 ,4 )` and an area of `16 pi`. Circle B has a center at `(12 ,8 )` and an area of `9 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

they don't over lap
the shortest distance between them is `sqrt(65) - 7 ~~` 1.062257748

Explanation:

area of Circle A = `pi*` `(Ra)^2`
16`pi` = `pi * Ra^2`
`Ra^2` = 16
Ra = 4

area of Circle B = `pi* Rb^2`
`9 pi` = `pi * Rb^2`
9 = `Rb^2`
Rb = 3

the distance between the center points is:
`sqrt((delta x)^2 + (delta y)^2)`
`delta x` = Xa - Xb = 5 - 12 = -7
`delta y` = Ya - Yb = 4 - 8 = -4
`sqrt((-7)^2 + (-4)^2)` = `sqrt(65)` `~~` 8.062257748

`because` Ra + Rb < `sqrt((delta x)^2 + (delta y)^2)`
`therefore` they didn't overlap.

the shortest distance between them is:
Gap = Distance between 2 center points - Ra - Rb
= `sqrt(65)` - 4 -3
`~~` 1.062257748

keep on learning~