# Circle A has a center at #(12 ,9 )# and an area of #25 pi#. Circle B has a center at #(3 ,1 )# and an area of #64 pi#. Do the circles overlap?

Yes

Finally we add these two radii together. The sum of the radii is 13, which is greater than the distance between the centers of the circle, meaning that the circles will overlap.

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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.

- Proof of the shortest distance from a point to a plane formula?
- Circle A has a center at #(1 ,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?
- What is the perimeter of a triangle with corners at #(3 ,8)#, #(1 ,5 )#, and #(4 ,3 )#?
- A triangle has corners at #(1 ,3 )#, #(9 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- Using the midpoint formula, if you're only given #((x_1 + x_2) / 2#, #(y_1 + y_2) / 2)#, is it possible to solve for #x# and #y#?

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