The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.
In general
$\displaystyle (R - \omega)^2 + (R - 2\omega)^2 = R^2 $
$\displaystyle R^2 - 2R( \omega + 2\omega ) + {\omega}^2( 1 + 2^2 ) = 0 $
$\displaystyle R^2 - 6R(\omega) + 5{\omega}^2 = 0 $
$\displaystyle ( R - 5 \omega )(R - \omega) = 0 $
Therefore , the relationship between $\displaystyle R $ and $\displaystyle \omega $ is
$\displaystyle R = 5\omega $
or their ratio is 5