The Area of a Square Inscribed in a Circle

Date: 12/23/95 at 15:41:22
From: Anonymous
Subject: GRE General question...

HELP!

I don't understand how this answer came to be! It comes from 
Cliff's GRE Prep Guide.

Q: What is the area of a square inscribed in a circle whose
 circumference is 16 (pi).

A: 128.

Response: Huh?! How'd they do that !?

Thank you very much,

	Thomas

Date: 12/23/95 at 17:48:58
From: Doctor Elise
Subject: Re: GRE General question...

Hi!  

The circumference of a circle is (pi) times the diameter, so we know the 
diameter of the circle is 16.  Since the square is inscribed in the 
circle, the diagonal distance between opposite corners is 16.  

a^2 + b^2 = c^2, where 'c' is the diagonal (which is 16) across the 
square, and forms the hypotenuse of a right triangle.  Since this is a 
square, we know that a = b.  So we know that a^2 + a^2 = (16)^2.  

And we can reduce this to a^2 = ((16)^2)/2 = 16 * 16/2 = 16 * 8 = 128.  
Since a^2 is the area of the square, we're done!

-Doctor Elise,  The Geometry Forum