A problem about two circles

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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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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$
$R = 8$

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