Inscribed Square

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smclean23: Master | Next Rank: 500 Posts; Posts: 172; Joined: Mon Jun 23, 2008 12:00 pm; Thanked: 3 times; Followed by:1 members

Inscribed Square

by smclean23 » Mon Aug 04, 2008 10:32 am

Let S be the length of the side of a square inscribed in a circle of radius R. Which of the following represents the ratio of the area of the circle to that of the square?

Pi/2
2r
Pi(r)
4Pi(r^2)
8Pi(r^2)

What is the methodology?

A

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Source: Beat The GMAT — Problem Solving | Mon Aug 04, 2008 10:32 am

eccentric: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Tue Jul 15, 2008 1:43 am; Thanked: 3 times; Followed by:1 members; GMAT Score:590

by eccentric » Mon Aug 04, 2008 10:42 am

The square inscribed in a circle has diagonal as diameter of circle.
The half of square makes a 45-45-90 triangle
with hyp as 2R
thus (2R)^2 = x^2+x^2 = 2x^2 area of square is 2R^2
and area of circle is pi R^2
thus ratio of area of circle to area of square is pi/2

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Gaurav Tyagi: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Jul 29, 2008 1:27 pm; Location: Santa CLara; Thanked: 1 times

Another way to look at it

by Gaurav Tyagi » Mon Aug 04, 2008 12:21 pm

A first look at this problem gives me an idea that any answer to this problem cannot contain any variable R or S as it is asking for a ratio of squares in which either both R and S should be there in the answer or none of them. Hence, I can eliminate b,c,d and e.

Thanks,

GT