Inside one circle there is another, which is smaller, which touches the first one at one point. The radius of the first circle is twice the radius of the second. Distance between centers of the circles is 4. Find the radius of the smaller circle.
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – CrSb0001 Sep 12 '23 at 18:07
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Is it not $4,?$ – Kurt G. Sep 12 '23 at 18:24
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Yeah, I think that the radius is 4 too. But the book says that the correct answer is 6. It's probably just a typo... – Тимофей Главицкий Sep 12 '23 at 18:29
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Sometimes a figure makes everything obvious:
David G. Stork
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In the book where this problem is written, the picture appears to be drawn incorrectly. There the center of the larger one is inside the smaller circle, and not on its circumference. I didn’t even think about the fact that if the radius is twice as large, then the center of the larger circle must lie on the circumference of the smaller one... – Тимофей Главицкий Sep 12 '23 at 19:58
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Big circle radius = $R$
Small circle radius =$r$
$R = 2r$
Distance between centers $c = 4$
$4 + r = R$ (c + radius of small circle)
$4 + r = 2r$
$ r = 4$
$R = 8$
Agent Smith
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Yeah, I think that the radius is 4 too. But the book says that the correct answer is 6. It's probably just a typo... – Тимофей Главицкий Sep 12 '23 at 18:35