A circle with center O is inscribed in square WXYZ. Point P is the int

Question

https://gmatclub.com/forum/download/file.php?id=19937 A circle with center O is inscribed in square WXYZ. Point P is the intersection between the circle and the line connecting O with X. If PX =\sqrt{2} - 1 , what is the approximate area of the shaded parts of the square? A. 0.5 B. 0.64 C. 0.85 D. 1 E. 1.25 Untitled.jpg

BukrsGmat · Answer

From the above figure OX =  \sqrt{2}  and OP = 1
so Area of circle =  pi*1*1= Pi

Diagonal XZ =  2*\sqrt{2} 
so side of square= 2 
area = 4

diff in area = 4 - 3.14 = 0.85

IMO: C

nave · Answer

Let side of the square be  a 
So, radius of the inscribed circle is  \frac{a}{2} = OP

OX = \frac{1}{2}*\sqrt{2}a

PX = OX - OP

i.e  \sqrt{2}-1 = \frac{1}{2}*\sqrt{2}a - \frac{a}{2}

i.e  2*(\sqrt{2}-1) = a*(\sqrt{2}-1)

So  a=2 ; area of the square is 4.

Area of a circle inscribed in a square is  \frac{pi}{4}*a^2  i.e in this instance the area of the circle is  pi  (since  a^2 = 4 )

The shaded portion is  \frac{ 3}{4 }*(4-pi) = \frac{3}{4}*0.86  which is approximately  0.64

Answer is B

nave · Answer

Please note that it is shaded only on 3 sides

mal208213 · Answer

Sujit,

I dont know how you got OX =  \sqrt{2}  and OP = 1. Could you break it down?

Also Nave is right question asks for shaded area and hence your answer needs to be multiplied by 3/4 or 0.75.

Thanks

kapilmba · Answer

1. OX is half of the diagonal of the square
2. radius of the circle is half of the side of the square
(sqrt(2)*a)/2 - a/2 = sqrt(2) - 1

this gives a = 2
and r = 1

Area of the square = 4

area of the circle = pi

Area of shaded portion = (Area of square - area of circle) *3/4

=.86*3/4 = .64

Bunuel · Answer

Similar questions to practice: a-circle-with-center-o-is-inscribed-in-square-wxyz-point-p-as-71413.html in-the-figure-above-a-circle-with-center-o-is-inscribed-in-the-square-190771.html

mvictor · Answer

tricky one.
so, we know PX. it can mean that OP=1 and OX=sqrt(2) or the diagonal of the square = 2(sqrt2). side of the square = 2. total area =4.
area of the circle = pi.

area of all 4 regions is ~ 4-pi or 3.14 => 0.86. now this is for all 4, we need to find area for 3 only:
0.86*3/4 ~ 0.64

72pala · Answer

I was able to deduce B in my head fairly quickly, and then when I saw your math, it confirmed my deduction. Thanks!

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A circle with center O is inscribed in square WXYZ. Point P is the int

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A circle with center O is inscribed in square WXYZ. Point P is the int

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