Circle A has a radius of 5 and a center of (3,2). Circle B has a radius of 2 and a center of (1,4). If circle B is translated by <2,−1>, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
Aug 6, 2018
Explanation:
What we have to do here is compare the distance (d)
to the sum/difference of radii
∙ if sum of radii>d then circles overlap
∙ if sum of radii<d then no overlap
∙ if difference of radii>d one circle inside other
Before calculating d we require to find the new centre
of B under the given translation
under the translation <2,−1>
(1,4)→(1+2,4−1)→(3,3)←new centre of B
calculate d using the distance formula
∙xd=√(x2−x1)2+(y2−y1)2
let (x1,y1)=(3,3) and (x2,y2)=(3,2)
d=√(3−3)2+(3−2)2=√1=1
sum of radii =5+2=7
difference of radii =5−2=3
since difference of radii>d circle B inside circle A
graph{((x-3)^2+(y-2)^2-25)((x-3)^2+(y-3)^2-4)=0 [-40, 40, -20, 20]}
