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# ABCD is a square and one of its sides AB is also a chord of the circle

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
ABCD is a square and one of its sides AB is also a chord of the circle  [#permalink]

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09 Oct 2018, 00:15
00:00

Difficulty:

25% (medium)

Question Stats:

83% (00:34) correct 17% (00:19) wrong based on 19 sessions

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ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

(A) 3

(B) 9

(C) 12

(D) 12√2

(E) 18

Attachment:

figure.jpg [ 30.59 KiB | Viewed 226 times ]

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GMAT 1: 640 Q44 V34
WE: Accounting (Consulting)
ABCD is a square and one of its sides AB is also a chord of the circle  [#permalink]

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Updated on: 09 Oct 2018, 00:26
Since the radii of the circle and the chord form a right angled triangle, the length of the chord becomes 3\sqrt{2}.

Further, the chord is the side of the square. Using the formula for the area of a square, the area is 3\sqrt{2}*3\sqrt{2}= 18 sq units. Answer E.

Originally posted by SushiVoyage on 09 Oct 2018, 00:22.
Last edited by SushiVoyage on 09 Oct 2018, 00:26, edited 1 time in total.
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Re: ABCD is a square and one of its sides AB is also a chord of the circle  [#permalink]

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09 Oct 2018, 00:24
Bunuel wrote:

ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

(A) 3

(B) 9

(C) 12

(D) 12√2

(E) 18

Attachment:
figure.jpg

AB is basically the side hypontuse of the triangle and side of a square.

$$AB^2 = 3^2 + 3^2$$
AB = $$\sqrt{18}$$

Area of the square = AB*AB = $$\sqrt{18*18}$$ = 18

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Joined: 07 Jan 2018
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Re: ABCD is a square and one of its sides AB is also a chord of the circle  [#permalink]

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09 Oct 2018, 00:44
OA^2+OB^2=AB^2-Using pythogoras theorem

Therefore, 3^2+3^2=AB^2
AB=√18=3√2
We've got one side of the square.
Area of the square= 3√2 × 3√2 =18

So the answer is option E

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Re: ABCD is a square and one of its sides AB is also a chord of the circle   [#permalink] 09 Oct 2018, 00:44
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