Circle A has a radius of $5$ $5$ and a center of $(2, 6)$ $(2 ,6 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 3)$ $(4 ,3 )$ . If circle B is translated by $< - 3, 2 >$ $<-3 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2017-08-18T02:44:56

The distance between the centers of the circles is $\sqrt{2}$ $sqrt2$ , and since the radius of circle a is 5, the circles will definitely overlap.

The new center of circle B will be $(4 - 3, 3 + 2) = (1, 5)$ $(4-3,3+2)=(1,5)$ .

We can now find the distance between the centres of the two circles:

$r = \sqrt{{(x_{a} - x_{b})}_{a}^{2} + {(y_{a} - y_{b})}_{a}^{2}}$ $r = sqrt((x_a-x_b)^2+(y_a-y_b)^2)$

$= \sqrt{{(x_{a} - x_{b})}_{a}^{2} + {(y_{a} - y_{b})}_{a}^{2}}$ $= sqrt((x_a-x_b)^2+(y_a-y_b)^2)$

$= \sqrt{{(2 - 1)}^{2} + {(6 - 5)}^{2}} = \sqrt{2} = 1.414$ $= sqrt((2-1)^2+(6-5)^2)=sqrt2=1.414$

Given that the radius of circle a is 5, the circles will definitely overlap.

Circle A has a radius of 55 and a center of (2,6)(2 ,6 ). Circle B has a radius of 22 and a center of (4,3)(4 ,3 ). If circle B is translated by <−3,2><-3 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?