# Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

circles have a single point of contact.

A translation does not change the shape of a figure , only it's position.

centre of B (5 , 3 ) → (5 -2 , 3+2) → (3 , 5)

now: radius of A + radius of B = 4 + 1 = 5

Since sum of radii = distance between centres , then the circles will have a single point of contact.

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The minimum distance between points on both circles is 3 units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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