# Circle A has a center at #(1 ,4 )# and a radius of #2 #. Circle B has a center at #(9 ,3 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

If the distance between centres is less than the sum of the radii then they overlap.

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Yes, the circles overlap. The smallest distance between them is 5 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.

- A triangle has corners at #(5 ,3 )#, #(9 ,7 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,3 )# to #(8 ,9 )# and the triangle's area is #36 #, what are the possible coordinates of the triangle's third corner?
- A triangle has corners at #(1 ,9 )#, #(7 ,8 )#, and #(4 ,5 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(7 ,5 )#, #(1 ,2 )#, and #(4 ,7 )#?
- A line passes through #(8 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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