Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #23

1

# In the figure above, O and P

In the figure above, O and P are the centers of the two circles. If each circle has radius r, what is the area of the shaded region?

### 1 Explanation

1 Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Ed Sia

Why is qp also r?

Jonathan , Magoosh Tutor

Hi Ed. because O and P are centers of the circles, OP is the length of a radius of the circles. Notice that QP is ALSO a radius. So it also equals r. I hope that helps.

excuse me, but... since both circles have radius r, then if we name the top dot A and the bottom one B, then, OA=AP=PB=OB = r WHICH MEANS SQUARE! aka: the shaded region's area is r^2

Cydney Seigerman, Magoosh Tutor

Hi there :)

You're correct that the 4 sides of the quadrilateral are of equal length. However, this does not necessarily mean that the shaded region is a square. Rather, this information guarantees that the shape is a rhombus (a quadrilateral with 4 equal sides). In order to be a square, the four angles would need to be equal to 90?. This is not the case: angle A = angle B = 60?while angle O = angle P = 150?.

Hope this helps :)