# Circle A has a radius of #1 # and a center at #(7 ,2 )#. Circle B has a radius of #3 # and a center at #(6 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

no overlap , ≈ 4.062

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

Before calculating d, we have to find the 'new' centre of circle B under the given translation which does not change the shape of the circle only it's position.

The 2 points here are (7 ,2) and (3 ,9)

Sum of radii = radius of A + radius of B = 1 + 3 = 4

Since sum of radii < d , then no overlap

min distance between points = d - sum of radii

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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 radius of #1 # and a center of #(2 ,4 )#. Circle B has a radius of #2 # and a center of #(4 ,5 )#. If circle B is translated by #<1 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(1, 6 )#, ( 1 , 2)#, and #( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment has endpoints at #(7 ,3 )# and #(1 ,2 )#. The line segment is dilated by a factor of #3 # around #(3 ,4 )#. What are the new endpoints and length of the line segment?
- Points A and B are at #(9 ,3 )# and #(7 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- Circle A has a radius of #2 # and a center of #(3 ,1 )#. Circle B has a radius of #6 # and a center of #(8 ,5 )#. If circle B is translated by #<-4 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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