Circle A has a radius of 1 and a center of (1 ,7 ). Circle B has a radius of 2 and a center of (8 ,1 ). If circle B is translated by <-4 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Feb 23, 2018

"no overlap "~~1.24

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 centre of B"
"under the given translation"

"under the translation "<-4,3>

(8,1)to(8-4,1+3)to(4,4)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)=(1,7)" and "(x_2,y_2)=(4,4)

d=sqrt((4-1)^2+(4-7)^2)=sqrt(9+9)=sqrt18~~4.24

"sum of radii "=1+2=3

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

"min. distance "=d-" sum of radii"

color(white)(xxxxxxxxxx)=4.24-3=1.24
graph{((x-1)^2+(y-7)^2-1)((x-4)^2+(y-4)^2-4)=0 [-20, 20, -10, 10]}