Question

Circle A has a center at `(2 ,3 )` and a radius of `1`. Circle B has a center at `(-1 ,-2 )` and a radius of `4`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

`therefore`Circles A and B do not intersect at all.

Explanation:

Two circles overlap if they intersect at two points .
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Two circle `A (O1,r1)" "and " " B (O2,r2)` intersect at two points
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`iff d(O1,O2) < r1+r2" "` where `" "d (O1,O2)` is the distance
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between the two centres.
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`d (O1,O2) = sqrt ((y_(O2)-y_(O1))^2 + (x_(O2)-X_(O1))^2)`
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`d (O1,O2) = sqrt((-2-3)^2+(-1-2)^2)`
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`d (O1,O2) = sqrt((-5)^2+(-3)^2)`
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`d (O1,O2) = sqrt(25+9)=sqrt34`
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Distance between the radii is:
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`r1+r2=1+4=5`
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`d (O1,O2)>r1+r2`
`" "`
`therefore`Circles A and B do not intersect at all.