Circle A has a radius of 4 and a center of (6 ,2 ). Circle B has a radius of 3 and a center of (5 ,7 ). If circle B is translated by <-2 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Jun 1, 2018

"no overlap "~~0.62

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"

"before calculating d we require to find the new centre"
"of B under the given translation"

"under a translation "< -2,2>

(5,7)to(5-2,7+2)to(3,9)larrcolor(red)"new centre of B"

"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)=(6,2)" and "(x_2,y_2)=(3,9)

d=sqrt((3-6)^2+(9-2)^2)=sqrt(9+49)=sqrt58~~7.62

"sum of radii "=4+3=7

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

"minimum distance "=d-" sum of radii"

color(white)(xxxxxxxxxxxxx)=7.62-7=0.62
graph{((x-6)^2+(y-2)^2-16)((x-3)^2+(y-9)^2-9)=0 [-20, 20, -10, 10]}