Question

Circle A has a radius of `4` and a center of `(8 ,5 )`. Circle B has a radius of `2` and a center of `(6 ,1 )`. If circle B is translated by `<2 ,7 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

`"circles overlap"`

Explanation:

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

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

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

`"before calculating d we require to find the 'new' coordinates"`
`"of centre B under the given translation which does not change"`
`" the shape of the circle only it's position"`

`"under a translation" ((2),(7))`

`(6,1)to(6+2,7+1)to(8,8)larr" new centre of B"`

`"to calculate d note the centres are " (8,5)" and " (8,8)`

`"the x-coordinates are equal so centres lie on a "`
`"vertical line and "`

`d=8-5=3`

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

`"since sum of radii ">d" then circles overlap"`
graph{(y^2-16y+x^2-16x+124)(y^2-10y+x^2-16x+73)=0 [-20, 20, -10, 10]}