# Circle A has a radius of 5  and a center of (3 ,2 ). Circle B has a radius of 3  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?

Nov 20, 2016

circle B inside circle A

#### Explanation:

What we have to do here is $\textcolor{b l u e}{\text{compare}}$ the distance ( d) between the centres of the circles to the $\textcolor{b l u e}{\text{sum/difference of the radii}}$

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

• If difference of radii > d , then one circle inside the other

Before calculating d we must find the ' new' centre of B under the given translation which does not change the shape of the circle only it's position.

Under a translation $\left(\begin{matrix}2 \\ - 1\end{matrix}\right)$

$\left(1 , 4\right) \to \left(1 + 2 , 4 - 1\right) \to \left(3 , 3\right) \leftarrow \text{ new centre of B}$

Since the centres (3 ,2) and (3 ,3) have the same x-coordinate they lie on the vertical line with equation x = 3 and d is the difference of the y-coordinates.

$\Rightarrow d = 3 - 2 = 1$