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

 It is currently 01 May 2016, 12:31

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 613
Location: PA
Followers: 3

Kudos [?]: 503 [1] , given: 22

If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

22 Mar 2011, 09:46
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

56% (01:58) correct 44% (01:14) wrong based on 62 sessions

### HideShow timer Statictics

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.
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2022
Followers: 154

Kudos [?]: 1418 [1] , given: 376

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

22 Mar 2011, 10:08
1
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"
_________________
SVP
Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 434 [0], given: 36

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

22 Mar 2011, 19:05
(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.

_________________

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

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 05 Jan 2011
Posts: 177
Followers: 3

Kudos [?]: 64 [0], given: 8

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

22 Mar 2011, 21:50
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
Joined: 22 Nov 2010
Posts: 12
Followers: 0

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

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

23 Mar 2011, 01:38
It’s C:
The answer is area of a circle, A=πr^2 =π( √(80/(√3)) )^2 here the radius is √(80/(√3))
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9248
Followers: 454

Kudos [?]: 115 [0], given: 0

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

28 Sep 2015, 08:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 06 Jun 2013
Posts: 52
Followers: 0

Kudos [?]: 3 [0], given: 174

Re: If a triangle inscribed in a circle has area 40, what is the [#permalink]

### Show Tags

28 Sep 2015, 08:44
i have a doubt in this question.

if we consider diameter as the base of the triangle, then opposite angle will be 90. in this case, two sides making the 90 degree angle will be base and height or vice versa. and in this case, diameter is the longest side. this diameter can not be the base as mentioned in the statement 1. hence E should be the option.

please explain where i am making mistake. i find statement 1 erroneous.
Re: If a triangle inscribed in a circle has area 40, what is the   [#permalink] 28 Sep 2015, 08:44
Similar topics Replies Last post
Similar
Topics:
If a circle is inscribed in an equilateral triangle, what is the area 4 29 Feb 2016, 10:42
20 In the figure shown, triangle ABC is inscribed in the circle. What is 3 02 Sep 2015, 03:59
5 If the circle has radius 6, what is the area of the triangle? (1) AC 10 26 Feb 2015, 06:45
What is the area of the innermost circle which is inscribed 7 23 Jan 2011, 03:11
7 What is the area of the parallelogram inscribed in a circle? 18 31 May 2008, 05:28
Display posts from previous: Sort by