# Circle A has a center at #(-5 ,8 )# and a radius of #4 #. Circle B has a center at #(-3 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

#Since sum of radii > d , then circles overlap. graph{(y^2-16y+x^2+10x+73)(y^2-6y+x^2+6x+2)=0 [-28.48, 28.47, -14.24, 14.24]}

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Yes, the circles overlap. The smallest distance between them is 2 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.

- Circle A has a center at #(5 ,4 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #9 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- The equations #{(y = c x^2+d, (c > 0, d < 0)),(x = a y^2+ b, (a > 0, b < 0)):}# have four intersection points. Prove that those four points are contained in one same circle ?
- Circle A has a center at #(8 ,1 )# and an area of #64 pi#. Circle B has a center at #(14 ,8 )# and an area of #48 pi#. Do the circles overlap?
- A triangle has corners at #(6 ,4 )#, #(7 ,5 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(8 ,1 )# and an area of #100 pi#. Circle B has a center at #(4 ,2 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

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