+0

tangent question

+1
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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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Q(a, 0)

Q(-1, 0)

Apr 4, 2021
#2
+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
+32402
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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
+1

But could the tangent not be something like this? How would I calculate then?

Apr 4, 2021
#5
+1441
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I think both of you are correct.  (At least regarding the word common  )

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?

Btw, the first answer is mine.

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