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# In the diagram above, O is the center of the circle and ACDE is a squa

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Math Expert
Joined: 02 Sep 2009
Posts: 56275
In the diagram above, O is the center of the circle and ACDE is a squa  [#permalink]

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07 Aug 2018, 05:22
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Difficulty:

25% (medium)

Question Stats:

73% (01:13) correct 27% (01:26) wrong based on 68 sessions

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In the diagram above, O is the center of the circle and ACDE is a square. What is the area of the square?

(1) the circle has a radius of 2

(2) angle ACB = 90°

Attachment:

GMAT_DS_Magoosh_161.png [ 11.68 KiB | Viewed 949 times ]

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Re: In the diagram above, O is the center of the circle and ACDE is a squa  [#permalink]

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07 Aug 2018, 06:12
Bunuel wrote:

In the diagram above, O is the center of the circle and ACDE is a square. What is the area of the square?

(1) the circle has a radius of 2

(2) angle ACB = 90°

Attachment:
GMAT_DS_Magoosh_161.png

(1) the circle has a radius of 2
Angle ACB will be 90 (angle subtended by a diameter on the circle=90)
AC^2=4^2-3^2
AC=root7
This should give us the area of the square

(2) angle ACB = 90°
AC however cannot be calculated
Insufficient

A it is !!
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Re: In the diagram above, O is the center of the circle and ACDE is a squa  [#permalink]

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07 Aug 2018, 06:41
(1) the circle has a radius of 2
Now, when a side of an inscribed triangle is the diameter of the circle , the opposite angle is 90
Two sides of the right angle triangle are known, using pythagoras theorem third angle can be calculated and area of the square can be found.
Sufficient

(2) angle ACB = 90°
No information about any other side of triangle
Insufficient

Hence, A.
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Re: In the diagram above, O is the center of the circle and ACDE is a squa  [#permalink]

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08 Aug 2018, 05:17
Bunuel wrote:

In the diagram above, O is the center of the circle and ACDE is a square. What is the area of the square?

(1) the circle has a radius of 2

(2) angle ACB = 90°

Attachment:
GMAT_DS_Magoosh_161.png

we are asked to find out the area of the square.

Note: Diameter of a circle is basically a hypotenuse of right triangle.

Statement : radius = 2, diameter = 4 . apply a^2 = b^2 + c^2 . therefore we will get the length of the one side of square. Sufficient.

Statement 2: we just know the ACB = 90 degree but we don't know the value of hypotenuse. Not Sufficient.

Re: In the diagram above, O is the center of the circle and ACDE is a squa   [#permalink] 08 Aug 2018, 05:17
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