SOLUTION: Two circles intersect at points V and W. The radius of the larger circle is 17, and the radius of the smaller circle is 10. Neither circle's center is inside the other circle. If t

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Question 328517: Two circles intersect at points V and W. The radius of the larger circle is 17, and the radius of the smaller circle is 10. Neither circle's center is inside the other circle. If the length of the vertical line VW is 16, what is the length of the segment connecting the circle's centers?
Found 2 solutions by solver91311, Fombitz:
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the center of the larger circle. Let represent the center of the smaller circle.

Let represent the point of intersection of the segments and .

First thing to notice is that is the mid-point of . The next thing to notice is that is a radius of circle . And that is a radius of circle . And finally, .

is the hypotenuse and is the short leg of a right triangle.



Likewise, is the hypotenuse and is the short leg of a right triangle.



And finally:



John

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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As you can see from the figure, a-8-10 and b-8-17 form right triangles.
Use the Pythagorean theorem to solve for a and b.
a%5E2%2B8%5E2=10%5E2
a%5E2=100-64
a=6
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b%5E2%2B8%5E2=17%5E2
b%5E2=289-64
b=15
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Let D be the distance between the circle centers.
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D=a%2Bb
highlight%28D=21%29