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# Can a circle be drawn, s that its CIRCUMFERENCE includes all

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Director
Joined: 03 Jul 2003
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Can a circle be drawn, s that its CIRCUMFERENCE includes all [#permalink]

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17 Feb 2004, 06:19
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Can a circle be drawn, s that its CIRCUMFERENCE
includes all four vertices of quadrilateral ?

1) All four sides of Quadrilateral are equal in
length.

2. Each of the interior angles of Quadrilateral
measures 90 degres.

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SVP
Joined: 30 Oct 2003
Posts: 1788

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Location: NewJersey USA

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17 Feb 2004, 09:19
I dont understand this question at all.

A quadrilaterral has total angles of 360 and can be enclosed in a circle.
I believe D should be the answer.

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Senior Manager
Joined: 23 Aug 2003
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17 Feb 2004, 09:23
Its C....its necessary to know the angle to be able to draw a circle around a quadrilateral.The sides of a quadrilateral may be equal but if the angles of the sides are obtuse or acute we can't draw a circle.

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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SVP
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17 Feb 2004, 09:26
well I understand the question now. All the vertices of Quadrilateral should lie on the circumference.

I am also modifying my post. An acute rohmbus will not fit in a circle such that all vertices lie on the circumference. Looks like B is the answer But I have a following doubt.

If you make a rectangle very thin then the circle has to have an infinite radius. Limit of width of rectangle -> 0 R -> infinity
Whereas if you make all sides equal and all the angles = 90 degrees then definitely you can draw a circle around it.

I am leaning towards C

Last edited by anandnk on 17 Feb 2004, 09:56, edited 1 time in total.

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Manager
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17 Feb 2004, 09:42
You can always draw a circle that circumscribes a rectangle. Can't you?

I go with B

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Senior Manager
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17 Feb 2004, 09:48
I will go with B as well. Draw any quadrilateral with all the angle = 90. You will always be able to draw a circle through all the vertices.

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17 Feb 2004, 09:48
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