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

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Manager
Joined: 14 Dec 2004
Posts: 117
Rectangle ABCD is inscribed in a circle as shown above. What [#permalink]

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26 Mar 2005, 09:12
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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, 10:20, edited 1 time in total.
Manager
Joined: 13 Oct 2004
Posts: 236

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26 Mar 2005, 10:19
It looks like the 2nd statement is incomplete?.
Manager
Joined: 14 Dec 2004
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26 Mar 2005, 10:22
I fixed the typo in the question....
GMAT Club Legend
Joined: 15 Dec 2003
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26 Mar 2005, 13:19
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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Joined: 13 Jun 2004
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26 Mar 2005, 21:10
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.
Intern
Joined: 21 Jan 2012
Posts: 18
Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink]

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26 Aug 2012, 12:56
Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??
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Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink]

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26 Aug 2012, 13:16
1
KUDOS
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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Intern
Joined: 21 Jan 2012
Posts: 18
Diagonal of the rectangle inscribed in a circle [#permalink]

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26 Aug 2012, 13:17
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??
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: Diagonal of the rectangle inscribed in a circle [#permalink]

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26 Aug 2012, 13:45
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??

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.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 21 Jan 2012
Posts: 18
Re: Rectangle ABCD is inscribed in a circle as shown above. What [#permalink]

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26 Aug 2012, 13:48
Thanks EvaJager. That's a very useful property!
_________________

If something helps, you must appreciate!
I'll regard
Kudos as appreciation.. Thanks

Re: Rectangle ABCD is inscribed in a circle as shown above. What   [#permalink] 26 Aug 2012, 13:48
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