The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.

Printable View

- Nov 11th 2009, 09:06 AMmastersFind the radius
The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.

- Nov 11th 2009, 04:51 PMJester
- Nov 11th 2009, 08:44 PMsimplependulum
- Nov 12th 2009, 04:00 AMmasters
- Nov 12th 2009, 05:54 AMWilmer
"If radius = 30 and rectangle is w by 2w, find w"

would have been "fun" (Nod) - Nov 14th 2009, 09:36 PMsimplependulum

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