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# O is the Center of the circle with Diameter 12

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

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10 Jul 2017, 03:25
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85% (hard)

Question Stats:

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

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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
[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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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

umg

Below is my take...
Attachments

111.jpg [ 1.79 MiB | Viewed 901 times ]

Kudos [?]: 292 [3], given: 41

Senior Manager
Joined: 18 Jun 2016
Posts: 267

Kudos [?]: 187 [0], given: 103

Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: O is the Center of the circle with Diameter 12 [#permalink]

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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

umg

Below is my take...

Ops! Yes. Sorry. Marked the wrong OA. Fixed it.
_________________

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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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10 Jul 2017, 11:23
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+B
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Re: O is the Center of the circle with Diameter 12 [#permalink]

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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

umg

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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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

umg

Below is my take...

How do we know angle C is 60 degrees?

and can u help me evaluating the outer equilateral triangle?

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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Senior Manager
Joined: 18 Jun 2016
Posts: 267

Kudos [?]: 187 [0], given: 103

Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: O is the Center of the circle with Diameter 12 [#permalink]

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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

How do we know angle C is 60 degrees?

and can u help me evaluating the outer equilateral triangle?

Here is the explanation..

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 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.

Kudos [?]: 187 [0], given: 103

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

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20 Aug 2017, 08:00

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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# O is the Center of the circle with Diameter 12

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