GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2019, 04:51 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A circular region centered at C is inscribed in equilateral

Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 21 Oct 2013
Posts: 408
A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

1
16 00:00

Difficulty:   65% (hard)

Question Stats: 68% (03:09) correct 32% (03:18) wrong based on 219 sessions

### HideShow timer Statistics

Attachment: Triangle.png [ 14.67 KiB | Viewed 3717 times ]

A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?

A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3
Math Expert V
Joined: 02 Sep 2009
Posts: 59675
Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

8
2
goodyear2013 wrote: A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?

A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3

One could also use following approach and solve this question in 30 seconds:

The area of the shaded region = 1/2*(the area of the triangle - the area of the sector) = 1/2*(12 - something with π) = 6 - something with π.

Only A and B fits this format, but A is negative, so we can discard it.

Also:
C: 12 - π√3 = ~7 too big for the area of the tiny shaded region (more than half of the area of the triangle).
D: 12 - 3π = ~3 too big for the area of the tiny shaded region (~1/4 of the area of the triangle).
E: 3 + π√3 = ~8 too big for the area of the tiny shaded region (more than half of the area of the triangle).

_________________
##### General Discussion
Manager  B
Joined: 14 Mar 2014
Posts: 142
GMAT 1: 710 Q50 V34 Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

1
goodyear2013 wrote:
Attachment:
Triangle.png

A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?
A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3

area of equilateral triangle = √3/4 * a* a = 12.
Area of Sector = 1/2 * Theta * [π/180] * r * r
Here r= Height of equilateral triangle = √3/2 * a

Area of shaded region = 1/2[12 - Area of sector] = 6-π√3
Board of Directors P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

I tried to go beyond logic, and see how to solve the problem...
anyone could help me find out where did I go wrong??
Attachments Triangle.png [ 34.97 KiB | Viewed 2447 times ]

Board of Directors P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

any expert to comment on the steps needed to solve the problem?
VeritasPrepKarishma, EMPOWERgmatRichC, mikemcgarry -would love to hear from you guys.
Math Expert V
Joined: 02 Aug 2009
Posts: 8302
Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

goodyear2013 wrote:
Attachment:
Triangle.png

A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?

A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3

Hi debbiem,
whenever you see these Qs, look how you can home on to the shaded region.
it is area of triangle - area of that sector of circle, and this should be div by 2 as there are two equal portions left over and we have to pick one of them..

area =$$\sqrt{3}/4*a^2 = 12$$..

Now the radius of circle is equal to altitude AND what is altitude of equilateral triangle = $$\sqrt{3}/2a$$

so area of sector, which is 60 degree = 1/6th of area of circle =$$\frac{1}{6} *pi*(\sqrt{3}/2*a)^2 = \frac{1}{6}*pi*\frac{3}{4}*a^2 = \frac{1}{6}*pi*\sqrt{3}*area-of-circle$$..

=> $$\frac{1}{6}*pi*\sqrt{3}*12 = 2\sqrt{3}*pi.$$.

area of shaded portion = 1/2( area of triangle - area of circle) = $$\frac{1}{2} (12-2\sqrt{3}*pi) = 6-\sqrt{3}*pi$$
B
_________________
Manager  B
Joined: 15 Nov 2017
Posts: 52
Re: A circular region centered at C is inscribed in equilateral  [#permalink]

### Show Tags

I keep ending up with 6 - πx^2. Could someone help explain how to do this problem? I am almost there but am doing something wrong since I keep ending up with this answer. Any insight would be appreciated. Thank you!

Bunuel wrote:
goodyear2013 wrote: A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?

A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3

One could also use following approach and solve this question in 30 seconds:

The area of the shaded region = 1/2*(the area of the triangle - the area of the sector) = 1/2*(12 - something with π) = 6 - something with π.

Only A and B fits this format, but A is negative, so we can discard it.

Also:
C: 12 - π√3 = ~7 too big for the area of the tiny shaded region (more than half of the area of the triangle).
D: 12 - 3π = ~3 too big for the area of the tiny shaded region (~1/4 of the area of the triangle).
E: 3 + π√3 = ~8 too big for the area of the tiny shaded region (more than half of the area of the triangle). Re: A circular region centered at C is inscribed in equilateral   [#permalink] 17 Jan 2019, 07:11
Display posts from previous: Sort by

# A circular region centered at C is inscribed in equilateral  