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A circle with a radius of 2 units has its center at (0, 0). A circle with a radius of 7 units has its center at (15, 0). A line tangent to both circles intersects the x-axis at (x, 0) to the right of the origin. What is the value of x?

 Mar 7, 2021
 #1
avatar+291 
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The green line has a length of 2, the blue line has a length of 7, and the red line has a length of 15.

Since the green line is parallel to the blue line, the 2 right triangles shown above must be similar to each other.

That means the smaller red length is just \(\frac{2}{9}\cdot15 = \boxed{\frac{10}{3}}\), which is the answer.

 Mar 7, 2021
 #2
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thanks!

ddocm  Mar 7, 2021

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