Circle A has a radius of $3$ $3$ and a center at $(3, 3)$ $(3 ,3 )$ . Circle B has a radius of $5$ $5$ and a center at $(1, 7)$ $(1 ,7 )$ . If circle B is translated by $< 2, 4 >$ $<2 ,4 >$ , 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 $3$ $3$ and a center at $(3, 3)$ $(3 ,3 )$ . Circle B has a radius of $5$ $5$ and a center at $(1, 7)$ $(1 ,7 )$ . If circle B is translated by $< 2, 4 >$ $<2 ,4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer

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Answer 1 · 2017-05-10T00:38:45

Yes, they do overlap.

Explanation:

The center of B after transformation is $(3, 11)$ $(3,11)$ . The new distance between the two centers is $\sqrt{{(3 - 3)}^{2} + {(11 - 4)}^{2}} = 7$ $sqrt((3-3)^2+(11-4)^2)=7$ . The sum of the radii is $3 + 5 = 8$ $3+5=8$ . Since Distance between centers $<$ $<$ Sum of radii, the two circles overlap.

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Circle A has a radius of $3$ $3$ and a center at $(3, 3)$ $(3 ,3 )$ . Circle B has a radius of $5$ $5$ and a center at $(1, 7)$ $(1 ,7 )$ . If circle B is translated by $< 2, 4 >$ $<2 ,4 >$ , 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 3 33 and a center at (3 ,3 )(3,3)(3 ,3 ). Circle B has a radius of 5 55 and a center at (1 ,7 )(1,7)(1 ,7 ). If circle B is translated by <2 ,4 ><2,4><2 ,4 >, 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 $3$ $3$ and a center at $(3, 3)$ $(3 ,3 )$ . Circle B has a radius of $5$ $5$ and a center at $(1, 7)$ $(1 ,7 )$ . If circle B is translated by $< 2, 4 >$ $<2 ,4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?