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# A rectangle is inscribed in a circle whose radius equals R.

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A rectangle is inscribed in a circle whose radius equals R. [#permalink]

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03 Oct 2004, 09:41
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A rectangle is inscribed in a circle whose radius equals R. If it is known that this rectangle is not a square, what could be the perimeter of that rectangle?

a. 4 x root2 x R

b. 3R

c. 5R

d. 6R

7. 3.14R
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03 Oct 2004, 10:16
D
A rectangle for a certain fixed diagonal has the minimum perimeter for a square.
Now consider a square ina circle with radius R.
Perimeter is 4R(2)^(1/2) = 4(1.414)R = 5.6R.
This implies there can be no rectangle with diagonal 2R ,whose perimeter is less than 5.65R.
We look at the choices given, clearly 6R is the only alternative.
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Franky
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03 Oct 2004, 12:05
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04 Oct 2004, 09:49
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