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?

1 Answer
Oct 25, 2017

thereforeCircles 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
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thereforeCircles A and B do not intersect at all.