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A Unit circle has center at (5,0) and second circle with a radius 2 units has its center at (11,0). A common tangent to both circles intersects x-axis at Q(a,0) what is value of a

 Apr 4, 2021
 #1
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0

Q(a, 0) 

 

Q(-1, 0)

smiley

 Apr 4, 2021
 #2
avatar+122 
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Hi,

 

Could you please explain how you arrived at the answer? I would like to understand how to solve these problems.

 

Thanks

 Apr 4, 2021
 #3
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This diagram should help

 

.

 

Use similar triangles to find where the line crosses the x-axis.

 Apr 4, 2021
edited by Alan  Apr 4, 2021
edited by Alan  Apr 4, 2021
 #4
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But could the tangent not be something like this? How would I calculate then?

 Apr 4, 2021
 #5
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+3

I think both of you are correct.  (At least regarding the word common  wink)

 

In Alan's case, the tangent is called a Common external tangent.    (or common direct tangent)

 

In your case, it's called a Common internal tangent.       (or common indirect tangent)

 

But if circles are tangent to each other, then there are 2 external and 1 internal tangent.

 

Which one of these two is more common? frown

 

Btw, the first answer is mine.laugh

jugoslav  Apr 5, 2021
edited by jugoslav  Apr 5, 2021

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