# Two circles have the following equations #(x -1 )^2+(y -7 )^2= 25 # and #(x +3 )^2+(y +3 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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The circles do not contain each other. The greatest possible distance between a point on one circle and another point on the other is the sum of their radii, which is 5 + 3 = 8 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 circle has a center at #(7 ,2 )# and passes through #(1 ,1 )#. What is the length of an arc covering #(3pi ) /4 # radians on the circle?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #( pi)/6 #, and the triangle's area is #32 #. What is the area of the triangle's incircle?
- A circle has a center that falls on the line #y = 2/9x +8 # and passes through # ( 3 ,1 )# and #(1 ,4 )#. What is the equation of the circle?
- How do you write an equation of a circle with center at (-2,-8), r=5?
- A circle has a chord that goes from #pi/4 # to #pi/2 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?

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