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# What is the area of circle O above?

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Math Expert
Joined: 02 Sep 2009
Posts: 56268
What is the area of circle O above?  [#permalink]

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22 Feb 2018, 20:42
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Difficulty:

5% (low)

Question Stats:

82% (01:30) correct 18% (02:03) wrong based on 67 sessions

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What is the area of circle O above?

(A) $$24\pi$$

(B) $$36\pi$$

(C) $$48\pi$$

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:

2018-02-23_0740.png [ 15.69 KiB | Viewed 801 times ]

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Re: What is the area of circle O above?  [#permalink]

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22 Feb 2018, 22:31
1
AC=OB, OB=6, area = pi*r2 , area = pi*6square , area = 36pi
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Re: What is the area of circle O above?  [#permalink]

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23 Feb 2018, 02:02
Bunuel wrote:

What is the area of circle O above?

(A) $$24\pi$$

(B) $$36\pi$$

(C) $$48\pi$$

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:
2018-02-23_0740.png

similar triangles ac=ob= 6

area = pi r^2 = 36 pi

(B) imo
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Joined: 22 May 2016
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What is the area of circle O above?  [#permalink]

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23 Feb 2018, 13:42
Bunuel wrote:

What is the area of circle O above?

(A) $$24\pi$$

(B) $$36\pi$$

(C) $$48\pi$$

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:
2018-02-23_0740.png

Quick solution: OABC is either a rectangle or a square.* Either way, diagonal lengths are equal.

Mentally draw another diagonal, from O to B.
AC = OB = radius = 6

Area of circle = $$\pi r^2 = 36\pi$$

*Three right angles = two sets of parallel and perpendicular lines with 4 right angles => the figure is a rectangle or a square. OR:

The figure OABC is a parallelogram with four right angles.
Three right angles are indicated. Their sum = 270°.
Quadrilateral's internal angles sum to 360°, and (360°-270°) = 90° = fourth angle. Four right angles in a quadrilateral create two sets of parallel and perpendicular lines. The figure is a square or a rectangle.

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Re: What is the area of circle O above?  [#permalink]

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23 Feb 2018, 14:41
didn't think much
suppose AC is r. then the area is 36pi. C,D, E are out right away.
even if the OC was the r, then OC would be equal to 3sqrt(3), and area would be 27. A is out
B is left
I didn't consider the OB to be equal to AC...i guess I just missed it, and it seemed easier for me to go with my POE method.
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Re: What is the area of circle O above?   [#permalink] 23 Feb 2018, 14:41
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