Associated Topics || Dr. Math Home || Search Dr. Math

### 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

```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search