Question

Circle A has a center at `(3 ,1 )` and a radius of `4`. Circle B has a center at `(9 ,8 )` and a radius of `2`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

no overlap, min distance`~~3.22`

Explanation:

What we have to do here is `color(blue)"compare"` the distance ( d ) between the centres of the circles to the `color(blue)"sum of 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(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))`
where`(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

`"the 2 points here are " (3,1)" and " (9,8)`

`"let " (x_1,y_1)=(3,1)" and " (x_2,y_2)=(9,8)`

`d=sqrt((9-3)^2+(8-1)^2)=sqrt(36+49)=sqrt85~~9.22`

`"sum of radii "=4+2=6`

`"since sum of radii "< d" then no overlap"`

`"min. distance between circles "=d-" sum of radii"`

`rArr"smallest distance "=9.22-6=3.22`
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