Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2015, 08:11
GMAT Club Tests

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a triangle inscribed in a circle has area 40, what is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Director
Director
User avatar
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 358 [1] , given: 22

If a triangle inscribed in a circle has area 40, what is the [#permalink] New post 22 Mar 2011, 08:46
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

57% (01:31) correct 43% (01:17) wrong based on 23 sessions
If a triangle inscribed in a circle has area 40, what is the area of the circle?

(1) The base of the triangle is equal to the diameter of the circle.
(2) The measure of one of the angles in the triangle is 30.
_________________

If the Q jogged your mind do Kudos me : )

1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2027
Followers: 142

Kudos [?]: 1210 [1] , given: 376

Re: triangle ds [#permalink] New post 22 Mar 2011, 09:08
1
This post received
KUDOS
rxs0005 wrote:
If a triangle inscribed in a circle has area 40, what is the area of the circle?

(1) The base of the triangle is equal to the diameter of the circle.
(2) The measure of one of the angles in the triangle is 30.


(1)
This statement tells us that the inscribed triangle is a right angled triangle.
Right angled triangle have three sides;
Two smaller sides and one hypotenuse.

Area = 1/2*(smaller side)*(bigger side)=40 if we assume that it is not an isosceles right triangle.

We know the radius = 1/2*(Diameter) = 1/2*(Hypotenuse) [Hypotenuse is referred as "BASE" in this statement]
Not Sufficient.

(2)
The measure of one of the angles in the triangle is 30.
We can make plenty such triangles with one angle as 30.
Not sufficient.

Combining both;

We know that the triangle is a right angled triangle with 30-90-60 as its angles.

The opposite sides will be in ratio: \(x:2x:\sqrt{3}x\)

\(Area = \frac{1}{2}*x*\sqrt{3}x=40\)
\(x^2=\frac{80}{\sqrt{3}}\)
\(x=\sqrt{\frac{80}{\sqrt{3}}}\)

\(Hypotenuse = Diameter = 2x= 2*\sqrt{\frac{80}{\sqrt{3}}}\)
\(Area = \pi*(\frac{Diameter}{2})^2=\pi*(\sqrt{\frac{80}{\sqrt{3}}})^2=\pi*\frac{80}{\sqrt{3}}\)

Sufficient.

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1676
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 374 [0], given: 36

Premium Member Reviews Badge
Re: triangle ds [#permalink] New post 22 Mar 2011, 18:05
(1) is not sufficient, as the height can be altered, and the area = 1/2 * b * h = 40, where the base can also vary and hence the area of circle will also vary, as base of triangle = diameter.

(2) If measure of one angle is 30, still we can't decide on the other sides (or angles), so not sufficient. FOr example, the base may or may not be the diameter.

(1) and (2) together, If the base is the Diameter, and one angle is 30 degrees, the triangle is a 30.60-90 right triangle with sides in the ratio

1:sqrt(3):2. Hypotenuse is the Diameter and it can be found as area of triangle = 40.

So Answer - C.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 05 Jan 2011
Posts: 178
Followers: 3

Kudos [?]: 40 [0], given: 8

Re: triangle ds [#permalink] New post 22 Mar 2011, 20:50
From one we know its a right angle triangle . To calculate area of circle we need to know the radius of the circle(i.e hypotenuse of a triangle (b*h=80) ).

From 2 : its 30:60 :90 triangle with ration 1: 3^1/2 :2
we know b*h=80 or x*3^1/2 x=80.. we get x here

hypotenuse =diameter of circle=2x ...once we know diameter we can calculate area of circle.

Thus c
Intern
Intern
avatar
Joined: 22 Nov 2010
Posts: 12
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: triangle ds [#permalink] New post 23 Mar 2011, 00:38
It’s C:
The answer is area of a circle, A=πr^2 =π( √(80/(√3)) )^2 here the radius is √(80/(√3))
Re: triangle ds   [#permalink] 23 Mar 2011, 00:38
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If the circle has radius 6, what is the area of the triangle? (1) AC Bunuel 7 26 Feb 2015, 05:45
1 A regular hexagon is inscribed in a circle. What is the area smartyman 2 02 Jul 2014, 00:03
4 Experts publish their posts in the topic Rectangle ABCD is inscribed in circle P. What is the area of AccipiterQ 3 21 Oct 2013, 07:36
Experts publish their posts in the topic What is the area of the innermost circle which is inscribed MichelleSavina 7 23 Jan 2011, 02:11
4 Experts publish their posts in the topic What is the area of the parallelogram inscribed in a circle? ritula 18 31 May 2008, 04:28
Display posts from previous: Sort by

If a triangle inscribed in a circle has area 40, what is the

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.