Circle A has a radius of 4 4 and a center of (7 ,3 )(7,3). Circle B has a radius of 2 2 and a center of (1 ,2 )(1,2). If circle B is translated by <2 ,3 ><2,3>, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
Apr 27, 2016
circles overlap
Explanation:
What we have to do here is calculate the distance (d) between the centres of A and B and compare this with the sum of the radii.
• If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
Under a translation of
((2),(3)) centre of B(1 ,2) → (1+2 , 2+3) → (3 ,5)
Calculate d using the
color(blue)" distance formula "
color(red)(|bar(ul(color(white)(a/a)color(black)( d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2))color(white)(a/a)|)))
where(x_1,y_1)" and " (x_2,y_2)" are 2 points " let
(x_1,y_1)=(7,3)" and " (x_2,y_2)=(3,5)
d=sqrt((3-7)^2+(5-3)^2)=sqrt(16+4)=sqrt20 ≈ 4.472 radius of A + radius of B = 4 + 2 = 6
Since sum of radii > d , circles overlap
