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# If points X and Y are two distinct points in the coordinate

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Senior Manager
Joined: 22 Jun 2006
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If points X and Y are two distinct points in the coordinate [#permalink]  24 Mar 2007, 10:30
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If points X and Y are two distinct points in the coordinate plane, which of the following can have more than one possible value?

A. The circumference of a circle with diameter XY.
B. The area of a square with diagonal XY.
C. The perimeter of a right iscosceles triangle with a leg XY.
D. The area of a circle with chord XY.
E. The area of an equilateral triangle with base XY.

I got this question on my Kaplan CAT.
I answered C but it turns out that D is the correct answer.

While I kind of understand it. It'd be great to see some reasoning for why C is wrong.[/img]
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Manager
Joined: 22 Feb 2007
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The triangle in C is right angled. hence the angle measures are fixed (45,45,90). Also, since one leg is of length XY, other has to be of same length resulting only 1 possible value for the hypotenuse. That means with the data given, this triangle is a rigid triangle with no changes in perimeter possible.
On the contrary, you can draw a circle with chord XY at many places by varying the size of the circle. Hence the attributes of circle can vary even with length XY fixed.
Senior Manager
Joined: 22 Jun 2006
Posts: 286
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Ya but in the triangle
It is possible that either XY is the hypotenuse or one of the equal sides

Shouldn't that make a difference?
Manager
Joined: 11 Mar 2007
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Nupurgupt, choice C specifies that XY is a leg...I understand it as "legs" are never the hypotenuse, they are the sides adjacent to the right angle.
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