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

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Answer 1 · 2016-10-10T18:25:13

The distance between the centers, $d \approx 6.3$ $d~~ 6.3$ , is less than the sum of their radii, $4 + 3 = 7$ $4 + 3 = 7$ , therefore, the circles overlap.

Explanation:

The translation moves the center of the circle to the point $(3, 9)$ $(3, 9)$ .

Compute the distance between the centers:

$d = \sqrt{{(5 - 3)}^{2} + {(3 - 9)}^{2}}$ $d = sqrt((5 - 3)^2 + (3 - 9)^2)$

$d = \sqrt{2^{2} + {(- 6)}^{2}}$ $d = sqrt(2^2 + (-6)^2)$

$d = \sqrt{4 + 36}$ $d = sqrt(4 + 36)$

$d = \sqrt{40}$ $d = sqrt(40)$

$d \approx 6.3$ $d~~ 6.3$

The distance between the centers, $d \approx 6.3$ $d~~ 6.3$ , is less than the sum of their radii, $4 + 3 = 7$ $4 + 3 = 7$ , therefore, the circles overlap.

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Circle A has a radius of $4$ $4$ and a center of $(5, 3)$ $(5 ,3 )$ . Circle B has a radius of $3$ $3$ and a center of $(1, 4)$ $(1 ,4 )$ . If circle B is translated by $< 2, 5 >$ $<2 ,5 >$ , 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 4 44 and a center of (5 ,3 )(5,3)(5 ,3 ). Circle B has a radius of 3 33 and a center of (1 ,4 )(1,4)(1 ,4 ). If circle B is translated by <2 ,5 ><2,5><2 ,5 >, 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 $4$ $4$ and a center of $(5, 3)$ $(5 ,3 )$ . Circle B has a radius of $3$ $3$ and a center of $(1, 4)$ $(1 ,4 )$ . If circle B is translated by $< 2, 5 >$ $<2 ,5 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?