Radius of circle inside a circle

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April 3rd 2009, 06:37 PM
nathan02079

Radius of circle inside a circle

I am stumped with this Grade 11 circle challenge.

I'm supposed to find 'r' but no measurements are given. Can I get clues?

http://img23.imageshack.us/img23/5686/findingr.jpg

thanks!!
April 3rd 2009, 11:08 PM
red_dog

$O$ =the center of the big circle. $O_1$ =the center of the small circle.

Let $OA, \ OB$ the radius tangent to the small circle. In the figure it seems that the radius are perpendicular.

Let $OC\perp OA$ .

In the triangle $OCO_1$ apply Pitagora:

$OO_1^2=OC^2+O_1C^2\Rightarrow (R-r)^2=r^2+r^2\Rightarrow r^2-2Rr-R^2=0\Rightarrow r=R(\sqrt{2}-1)$

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