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O is the Center of the circle with Diameter 12

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O is the Center of the circle with Diameter 12 [#permalink]

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New post 10 Jul 2017, 03:25
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Difficulty:

  85% (hard)

Question Stats:

60% (02:05) correct 40% (02:19) wrong based on 80 sessions

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Attachment:
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O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
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[Reveal] Spoiler: OA

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Last edited by umg on 10 Jul 2017, 10:58, edited 1 time in total.

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 10 Jul 2017, 08:36
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umg wrote:
Attachment:
The attachment Untitled.png is no longer available

O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
Self Made


umg

can u please confirm the answer!!!

Below is my take...
Attachments

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 10 Jul 2017, 11:00
rohit8865 wrote:
umg wrote:
Attachment:
Untitled.png

O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
Self Made


umg

can u please confirm the answer!!!

Below is my take...

Ops! Yes. Sorry. Marked the wrong OA. Fixed it.
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I'd appreciate learning about the grammatical errors in my posts

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My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

Rest of the Notes coming soon.

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 11 Jul 2017, 12:32
rohit8865 wrote:
umg wrote:
Attachment:
Untitled.png

O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
Self Made


umg

can u please confirm the answer!!!

Below is my take...




How do we know angle C is 60 degrees?


and can u help me evaluating the outer equilateral triangle?

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 11 Jul 2017, 13:03
rocko911 wrote:
rohit8865 wrote:
umg wrote:
Attachment:
Untitled.png

O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
Self Made


umg

can u please confirm the answer!!!

Below is my take...




How do we know angle C is 60 degrees?


and can u help me evaluating the outer equilateral triangle?

in Quad AOBC

as we found angle BOD to 120
therefore, Angle AOB is 60

also as CB|| AD, therfore angle CBO = angle BOD

and similarly ang(CAO)= angle AOE= 120 degress

now in quad you have 3 angles so forth comes out be 60 by summing four angles to 36p

Sent from my SM-A700FD using GMAT Club Forum mobile app

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 13 Jul 2017, 01:48
rocko911 wrote:
umg wrote:
Attachment:
Untitled.png

O is the Center of the circle with Diameter 12 and length of arc BOD is \(4\pi\). What is the area of quadrilateral AOBC if AD is parallel to CB and BE is parallel to CA. (Figure not drawn to scale)

A. \(12\sqrt{3}\)
B. \(18\sqrt{3}\)
C. \(36\sqrt{3}\)
D. \(72\sqrt{3}\)
E. \(144\sqrt{3}\)



[Reveal] Spoiler: Source of Question
Self Made




How do we know angle C is 60 degrees?


and can u help me evaluating the outer equilateral triangle?

Here is the explanation..

In Quad AOBC,

AO // BC
BO // CA

So, this is a Parallelogram. Hence, it can be a square, rectangle, or rhombus. We know that

Angle AOB = 60
Hence, it is not a Square or Rectangle. Moreover, to prove that this is a Rhombus,

OA = OB :arrow: Radii of Circle.

Because Adjacent sides of a Rhombus are Equal, Quad AOBC is definitely a Rhombus.

Opposite angles of Rhombus are equal. Hence,

Angle AOB = Angle ACB = 60

Join AB and we have 2 equilateral Triangles. Find the area of one and multiply it by 2.



BTW, this is a special kind of Rhombus for which we do not need the lengths of diagonals to calculate the area.
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

Rest of the Notes coming soon.

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Re: O is the Center of the circle with Diameter 12 [#permalink]

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New post 20 Aug 2017, 08:00
Answer is B.


as it is clearly visible from pic, the area is 18√3
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Re: O is the Center of the circle with Diameter 12   [#permalink] 20 Aug 2017, 08:00
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