Find the radius

**masters** · November 11th 2009, 09:06 AM

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

**Danny** · November 11th 2009, 04:51 PM

Originally Posted by masters

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

$R = 30$ , No?

**simplependulum** · November 11th 2009, 08:44 PM

Originally Posted by Danny

$R = 30$ , No?

I think your answer is correct

$(R-6)^2 + (R-12)^2 = R^2$

$R^2 - 36R + 180 = 0$

$(R-30)(R-6) = 0$

but $R$ cannot be $6$ so the answer is 30

**masters** · November 12th 2009, 04:00 AM

Originally Posted by masters

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

Originally Posted by Danny

$R = 30$ , No?

Originally Posted by simplependulum

I think your answer is correct

$(R-6)^2 + (R-12)^2 = R^2$

$R^2 - 36R + 180 = 0$

$(R-30)(R-6) = 0$

but $R$ cannot be $6$ so the answer is 30

Very good, guys! I didn't want to stress your brains too much, so this one was not a really big challenge. I'll spice it up a little more in the future.

**Wilmer** · November 12th 2009, 05:54 AM

"If radius = 30 and rectangle is w by 2w, find w"
would have been "fun"

**simplependulum** · November 14th 2009, 09:36 PM

Originally Posted by Wilmer

"If radius = 30 and rectangle is w by 2w, find w"
would have been "fun"

In general

$(R - \omega)^2 + (R - 2\omega)^2 = R^2$

$R^2 - 2R( \omega + 2\omega ) + {\omega}^2( 1 + 2^2 ) = 0$

$R^2 - 6R(\omega) + 5{\omega}^2 = 0$

$( R - 5 \omega )(R - \omega) = 0$

Therefore , the relationship between $R$ and $\omega$ is

$R = 5\omega$

or their ratio is 5

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