Circle A has a radius of 2 2 and a center at (3 ,6 )(3,6). Circle B has a radius of 5 5 and a center at (2 ,3 )(2,3). If circle B is translated by <-2 ,1 ><−2,1>, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
circles overlap.
Explanation:
What we have to do here is compare the distance (d) between the centres of the circles to the sum of the radii.
• If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
The first step is to find the new centre of B under the translation. A translation does not change the shape of a figure , only it's position.
Under a translation of
((-2),(1)) centre B(2 ,3) → (2-2 ,3+1) → B(0 ,4)-(new centre)
To calculate the distance (d) between the centres use 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" The 2 points here being the centres of A and B.
let
(x_1,y_1)=(3,6)" and " (x_2,y_2)=(0,4)
d=sqrt((0-3)^2+(4-6)^2)=sqrt(9+4)=sqrt13≈3.606 radius of A + radius of B = 2 + 5 = 7
Since sum of radii > d , then circles overlap.
