# Circle A has a radius of 1  and a center of (1 ,2 ). Circle B has a radius of 2  and a center of (5 ,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?

Apr 22, 2016

circles overlap.

#### Explanation:

What we have to do here is calculate the distance (d) between the centres of the 2 circles and compare this distance with the sum of the radii.

• If sum of radii > d , then circles will overlap.

• If sum of radii < d , then no overlap.

Find the new position of centre of B , to begin with.

Under a translation of $\left(\begin{matrix}- 4 \\ 3\end{matrix}\right)$

centre of B (5 , 1) → (5-4 , 1+3) → (1 , 4)

Note that since the centres (1 ,2) and (1 ,4) have the same x-coordinate then they lie on the vertical line x = 1 and the distance (d) between them is the difference in their y-coordinates.
ie. d = 4 - 2 = 2

radius of A + radius of B = 1 + 2 = 3

Since sum of radii > d , then circles overlap.
graph{(y^2-4y+x^2-2x+4)(y^2-8y+x^2-2x+13)=0 [-10, 10, -5, 5]}