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There are two circles with radii 2 and 6. The centers of the circles are 10 units apart. What is the distance between the two tangency points as seen in the diagram?

 Dec 13, 2023
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Let's call the centers of the circles A and B, and let the tangency points be C and D, as shown in the diagram below:

 

Since the radii of the circles are 2 and 6, AC=2 and BD=6. Also, AB=10, since the centers of the circles are 10 units apart.

 

Triangle ABD is a right triangle, so by the Pythagorean Theorem, AD=AB2−BD2​=102−62​=64​=8.

 

Therefore, the distance between the two tangency points C and D is 8​ units.

 Dec 18, 2023

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