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Rectangle ABCD is inscribed in a circle as shown above. What

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Rectangle ABCD is inscribed in a circle as shown above. What [#permalink] New post 26 Mar 2005, 08:12
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Rectangle ABCD is inscribed in a circle as shown above. What is the radius of the circle?

(1) The length of the rectangle is sqrt(3) and the width of the rectangle is 1.
(2) The length of arc AB is 1/3 of the circumference of the circle.
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Last edited by cloaked_vessel on 26 Mar 2005, 09:20, edited 1 time in total.
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 [#permalink] New post 26 Mar 2005, 09:19
It looks like the 2nd statement is incomplete?.
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 [#permalink] New post 26 Mar 2005, 09:22
I fixed the typo in the question....
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 [#permalink] New post 26 Mar 2005, 12:19
A it is
1) Knowing 2 sides of an inscribed rectangle will give us length of hypothenuse aka radius which would be equal to 2
2) this gives us nothing as to length of hypothenuse because the circle could be of any size
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 [#permalink] New post 26 Mar 2005, 20:10
A too

Radius of the cercle could be AC/2 or BD/2, the diagonals of the rectangle.

with statement 1 you can use BA^2 + BC^2 = AC^2 and then find the solution because we have BA and BC

with statement 2, no information with values.
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Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink] New post 26 Aug 2012, 11:56
Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??
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Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink] New post 26 Aug 2012, 12:16
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ExuberantRahul wrote:
Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??


Yes. Any right triangle can be inscribed in a circle, having the hypotenuse its diameter.
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Diagonal of the rectangle inscribed in a circle [#permalink] New post 26 Aug 2012, 12:17
Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??


I was solving the below question:
http://gmatclub.com/forum/rectangle-abcd-is-inscribed-in-a-circle-as-shown-above-what-15182.html#p1116066

Rectangle ABCD is inscribed in a circle as shown above. What is the radius of the circle?

(1) The length of the rectangle is sqrt(3) and the width of the rectangle is 1.
(2) The length of arc AB is 1/3 of the circumference of the circle.


I got C as an answer assuming that the diagonal need not be the diameter. Please clarify whether the diagonal of the rectangle inscribed in a circle always the diameter of the circle??
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Re: Diagonal of the rectangle inscribed in a circle [#permalink] New post 26 Aug 2012, 12:45
ExuberantRahul wrote:
Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??


I was solving the below question:
http://gmatclub.com/forum/rectangle-abcd-is-inscribed-in-a-circle-as-shown-above-what-15182.html#p1116066

Rectangle ABCD is inscribed in a circle as shown above. What is the radius of the circle?

(1) The length of the rectangle is sqrt(3) and the width of the rectangle is 1.
(2) The length of arc AB is 1/3 of the circumference of the circle.


I got C as an answer assuming that the diagonal need not be the diameter. Please clarify whether the diagonal of the rectangle inscribed in a circle always the diameter of the circle??


The answer is A.

And Yes. Any right triangle can be inscribed in a circle, having the hypotenuse its diameter. The diagonal and two adjacent sides of a rectangle form a right triangle which can be inscribed in a circle having the diagonal=hypotenuse as diameter.
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Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink] New post 26 Aug 2012, 12:48
Thanks EvaJager. That's a very useful property! :)
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Re: Rectangle ABCD is inscribed in a circle as shown above. What   [#permalink] 26 Aug 2012, 12:48
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