Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jul 28 07:00 PM EDT  08:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Sunday, July 28th at 7 PM EDT
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 830
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
09 May 2015, 02:52
Question Stats:
67% (02:32) correct 33% (02:43) wrong based on 94 sessions
HideShow timer Statistics
If P is the center of the circle shown above, and BAC=30º, and the area of triangle ABC is 6, what is the area of the circle? A. (√3)π B. (2√3)π C. 4π D. 6π E. (4√3)π Attachment:
T6107.png [ 7.89 KiB  Viewed 1797 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Manager
Joined: 05 Feb 2015
Posts: 50
Concentration: Finance, Entrepreneurship
WE: Information Technology (Health Care)

Re: If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
09 May 2015, 03:55
triangle in a circle with 1 side as diameter is a right angle triangle. So, this is a 306090 triangle with sides in the ratio 1:sqrt3:2 area of ABC= 1/2*BC*AB = 1/2*r*sqrt3*r and this is given as 6 So, r^2=12/sqrt3 area of circle = pi*r^2 = pi*12/sqrt3 = 4*sqrt3*pi Answer is E



Manager
Joined: 27 May 2014
Posts: 79

Re: If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
09 May 2015, 05:43
Why is BA the height?



Manager
Joined: 05 Feb 2015
Posts: 50
Concentration: Finance, Entrepreneurship
WE: Information Technology (Health Care)

Re: If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
09 May 2015, 05:47
bankerboy30 wrote: Why is BA the height? As angle B is 90, the side opposite to it is the largest side i.e. the hypotenuse. So, other 2 sides are base and height. Hope it helps..



Intern
Joined: 16 Mar 2012
Posts: 9

Re: If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
30 Apr 2016, 14:58
Naina1 wrote: bankerboy30 wrote: Why is BA the height? As angle B is 90, the side opposite to it is the largest side i.e. the hypotenuse. So, other 2 sides are base and height. Hope it helps.. Agreed, that BA is the height but shouldnt the area be 1/2*AB (height) *BC?? Which should make it 1/2*2r*r =6 r^2=6 Does this not make the area to be 6PI ???? Please tell me where I'm going wrong



Math Expert
Joined: 02 Aug 2009
Posts: 7763

Re: If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
30 Apr 2016, 21:25
gmater12 wrote: Naina1 wrote: bankerboy30 wrote: Why is BA the height? As angle B is 90, the side opposite to it is the largest side i.e. the hypotenuse. So, other 2 sides are base and height. Hope it helps.. Agreed, that BA is the height but shouldnt the area be 1/2*AB (height) *BC?? Which should make it 1/2*2r*r =6 r^2=6 Does this not make the area to be 6PI ???? Please tell me where I'm going wrong Hi, You are correct upto a point.. But what is Height AB, It is NOT 2r.. Because 2r means DIAMETER and that is AC.. Now how do you find AB and BC when what you know is ONLY AC as 2r.. Triangle ABC is 306090 which gives sides opposite to these angles in ratio\(1:\sqrt{3}:2\).. Now Opposite 90 angle is HYP or AC or 2r.. so other sides \(= 1*r:\sqrt{3}*r:2*r\).. so \(AB = \sqrt{3}r\) and BC = r.. \(area = 1/2 *AB*BC = 1/2 *r*\sqrt{3}=6\).. \(r^2 = 12/\sqrt{3} = 4\sqrt{3}\).. so Area of circle = \(4\sqrt{3}*pi\) E
_________________



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2821

If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
Show Tags
22 Feb 2018, 09:24
reto wrote: If P is the center of the circle shown above, and BAC=30º, and the area of triangle ABC is 6, what is the area of the circle? A. (√3)π B. (2√3)π C. 4π D. 6π E. (4√3)π Recall that any triangle inscribed in a circle that has the diameter of the circle as its hypotenuse is a right triangle. Thus, triangle ABC is a 306090 right triangle, with the ratio of its sides as x : 2x: x√3.. Noting that the figure is not drawn to scale, we let side AB = x and side BC = x√3, and thus: x * x√3 * 1/2 = 6 x^2(√3) = 12 x^2 = 12/√3 x^2 = 12√3/3 x^2 = 4√3 Notice that AC, the diameter, is 2x. Thus the radius, AP or CP, is x, and hence the area of the circle, is πx^2. Since x^2 = 4√3, then the area of the circle is (4√3)π. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




If P is the center of the circle shown above, and BAC=30º, and the are
[#permalink]
22 Feb 2018, 09:24






