I am stumped with this Grade 11 circle challenge.
I'm supposed to find 'r' but no measurements are given. Can I get clues?
thanks!!
$\displaystyle O$=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:
$\displaystyle OO_1^2=OC^2+O_1C^2\Rightarrow (R-r)^2=r^2+r^2\Rightarrow r^2-2Rr-R^2=0\Rightarrow r=R(\sqrt{2}-1)$