Circle A has a radius of 4 and a center at (8,2). Circle B has a radius of 3 and a center at (4,5). If circle B is translated by <−3,4>, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
Jul 31, 2018
Explanation:
What we have to do here is to compare the distance (d)
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 <−3,4>
(4,5)→(4−3,5+4)→(1,9)←new centre of B
to calculate d use the distance formula
∙xd=√(x2−x1)2+(y2−y1)2
let (x1,y1)=(8,2) and (x2,y2)=(1,9)
d=√(1−8)2+(9−2)2=√49+49=√98≈9.9
sum of radii =4+3=7
since sum of radii<d then no overlap
minimum distance =d− sum of radii
××××××x=9.9−7=2.9
graph{((x-8)^2+(y-2)^2-16)((x-1)^2+(y-9)^2-9)=0 [-20, 20, -10, 10]}
