# Circle A has a center at #(2 ,4 )# and a radius of #9 #. Circle B has a center at #(1 ,-5 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

The two circles intersect.

Note : If the distance had been less than the difference of the two radii, thee smaller circle would have been entirely inside the larger one. On the other hand, had it been larger than the sum of the radii, the two circles would have been too far away to intersect. Neither is the case here.

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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.

- What are two lines in the same plane that intersect at right angles?
- Circle A has a center at #(11 ,2 )# and an area of #100 pi#. Circle B has a center at #(7 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- Are the planes #x+y+z=1# , #x-y+z=1# parallel, perpendicular, or neither? If neither, what is the angle between them?
- Circle A has a center at #(5 ,1 )# and an area of #23 pi#. Circle B has a center at #(2 ,8 )# and an area of #15 pi#. Do the circles overlap?
- A triangle has corners at #(9 ,3 )#, #(7 ,5 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

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