BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

To find the area of the circle

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

To find the area of the circle

by gmattesttaker2 » Sun Dec 01, 2013 7:09 pm
Hello,

Can you please assist with this:

In the figure above, circle O has its center on the intersection of the two
diagonals of square ABCD. What is the area of circle O if y is the measure of the
diagonal of each of the small squares in the figure and PQ = RS = TU = VW?

(1) y = 3√2
(2) PQ = 5

OA: B
Attachments
Circle area.png
Top
Source: — Data Sufficiency |
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Sun Dec 01, 2013 10:57 pm
Here's a (crude) attempt to draw and label the figure

Image

The basic idea:

* If the diagonal of the little squares is y, the sides of those squares are y/√2, or (y√2)/2, in proper form.

* Since the diagonal of the big square is (2r + 2y), the sides of that square are (2r + 2y)/√2, or √2(r+y), in proper form.

* Since the sides of the smaller squares sum to y√2, the distance between those squares on the sides of the big square is r√2 (i.e. PQ = r√2).

* Once you know r√2, you can find r, the radius of the circle, and solve.

* Since S2 gives you r√2, it's sufficient. Since S1 doesn't, it's not.
Top
Post new topic Post Reply
• Page 1 of 1