Circle A has a radius of $2$ $2$ and a center of $(8, 6)$ $(8 ,6 )$ . Circle B has a radius of $3$ $3$ and a center of $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 1, 2 >$ $<-1 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Circle A has a radius of $2$ $2$ and a center of $(8, 6)$ $(8 ,6 )$ . Circle B has a radius of $3$ $3$ and a center of $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 1, 2 >$ $<-1 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2016-04-09T20:54:35

no overlap , d ≈ 2.07

Explanation:

A translation does not change the shape of a figure , only it's position.

Under a translation of $((-1),(2))$

centre of circle B (2 , 3 ) → (2 -1 , 3 + 2) → (1 , 5)

Now, require to calculate the distance between the centres of A and B , using the $color(blue)" distance formula "$

$d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2$

where $(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "$

let $(x_1,y_1)=(8,6)" and " (x_2,y_2)=(1,5)$

d $= sqrt((1-8)^2 + (5-6)^2) = sqrt(49 + 1) = sqrt50 ≈ 7.07$

now, radius of A + radius of B = 2 + 3 = 5

Since sum of radii < distance between centres , no overlap.

and distance (d) between circles = 7.07 - 5 = 2.07

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Circle A has a radius of $2$ $2$ and a center of $(8, 6)$ $(8 ,6 )$ . Circle B has a radius of $3$ $3$ and a center of $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 1, 2 >$ $<-1 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Explanation:

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Circle A has a radius of 2 22 and a center of (8 ,6 )(8,6)(8 ,6 ). Circle B has a radius of 3 33 and a center of (2 ,3 )(2,3)(2 ,3 ). If circle B is translated by <-1 ,2 ><−1,2><-1 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer

Explanation:

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Circle A has a radius of $2$ $2$ and a center of $(8, 6)$ $(8 ,6 )$ . Circle B has a radius of $3$ $3$ and a center of $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 1, 2 >$ $<-1 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?