To find the area of the circle

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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

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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.