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QCircles

by nycknicks11 » Sun May 29, 2011 4:33 am
Two questions here:

1) Can you assume that the arc here is generated by a 1/4 of a circle? ("Arc is centered at C")

2) If its not, I don't see how the arc is relevant in this problem

Here's how I solved it (assuming 1/4 circle).

a) Since its part of the circle then the radius is 8
b) Since the diagonal of the large square is 8root(2)
c) The diagonal of the small square is root(2)
d) Thus the sides are 1 each
e) Thus area is 1.
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by vineeshp » Sun May 29, 2011 4:57 am
Hey,

Yes the arc is 1/4.
The circle is passing through the points B,D. So the radius of circle is the side of the large square.

In your calculation,
you have identified that the diagonal of larger circle is 8 root2. THis is correct. But I think you got the diagonal of smaller square wrong.

The diagonal should be 8root2 - 8.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by SoCan » Sun May 29, 2011 8:50 am
nycknicks11 wrote: a) Since its part of the circle then the radius is 8
b) Since the diagonal of the large square is 8root(2)
c) The diagonal of the small square is root(2)
d) Thus the sides are 1 each
e) Thus area is 1.
8sqr(2)-8 does not equal sqr(2). The most you can simplify it is: 8(sq(2)-1), but it's easiest keep it in the 8sqr(2)-8 form to solve the question. From there, you could either figure out the side of the smaller square, or just square the diagonal and divide by two. The former is messy and more time consuming.

Squaring the diagonal gives:
192-128sqr(2) = 64(3-2sqr(2)). Dividing by 2 gives 32(3-2sqr(2)).

You do raise an interesting point about the arc though. It never says the arc is part of a circle, and arc generally isn't defined as being part of a circle. An arc can be a segment of an ellipse, parabola, or any 2d curve. Perhaps for the GMAT, an arc is always part of a circle - would be great to get some clarity from an expert. My guess, though, is that that part is just poorly worded.
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