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!!

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- Apr 3rd 2009, 06:37 PMnathan02079Radius 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!! - Apr 3rd 2009, 11:08 PMred_dog
$\displaystyle O$=the center of the big circle. $\displaystyle O_1$=the center of the small circle.

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

Let $\displaystyle OC\perp OA$.

In the triangle $\displaystyle OCO_1$ apply Pitagora:

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