Circle A has a radius of $2$ $2$ and a center of $(2, 7)$ $(2 ,7 )$ . Circle B has a radius of $6$ $6$ and a center of $(7, 5)$ $(7 ,5 )$ . If circle B is translated by $< - 1, 1 >$ $<-1 ,1 >$ , 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 $(2, 7)$ $(2 ,7 )$ . Circle B has a radius of $6$ $6$ and a center of $(7, 5)$ $(7 ,5 )$ . If circle B is translated by $< - 1, 1 >$ $<-1 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-07T13:12:20

circle B do not overlap.
Shortest distance is $3.764 - 2 = 1.764$ $3.764-2=1.764$

Explanation:

Circle A
Center $(2, 7)$ $(2,7)$
radius $2$ $2$

Equation of circle A
${(x - 2)}^{2} + {(y - 7)}^{2} = 2^{2}$ $(x-2)^2+(y-7)^2=2^2$

Circle B
Center $(7, 5)$ $(7,5)$
radius $6$ $6$

Equation of circle B
${(x - 7)}^{2} + {(y - 5)}^{2} = 6^{2}$ $(x-7)^2+(y-5)^2=6^2$

ranslation of B
<-1,1>
Center of B after translation $((7-1),(5+1))$
Center of B after translation $(6,6)$

Equation of circle B after translation
$(x-6)^2+(y-6)^2=6^2$

Intersection of the circles
$(x-2)^2+(y-7)^2=2^2$
and
$(x-6)^2+(y-6)^2=6^2$
can be found out

Distance from center of Circle A to
center of Circle B is
$(2,7) ---- (6,6)$
$=sqrt((6-7)^2+(6-2)^2$
$=sqrt((1+4)$
$=sqrt(5)$
$=2.236$

Radius of circle A is $2$
point on the Perimeter of the circle B is away from its center by 6
point on the Perimeter of the circle B is away from (2,7) is $6-2.236$
$=3.764$
Hence, the two circles donot overlap.
Shortest distance is $3.764-2=1.764$

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Circle A has a radius of $2$ $2$ and a center of $(2, 7)$ $(2 ,7 )$ . Circle B has a radius of $6$ $6$ and a center of $(7, 5)$ $(7 ,5 )$ . If circle B is translated by $< - 1, 1 >$ $<-1 ,1 >$ , 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 22 and a center of (2 ,7 )(2,7)(2 ,7 ). Circle B has a radius of 6 66 and a center of (7 ,5 )(7,5)(7 ,5 ). If circle B is translated by <-1 ,1 ><−1,1><-1 ,1 >, 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 $(2, 7)$ $(2 ,7 )$ . Circle B has a radius of $6$ $6$ and a center of $(7, 5)$ $(7 ,5 )$ . If circle B is translated by $< - 1, 1 >$ $<-1 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?