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Quant Review #153

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lsegal
 Post subject: Quant Review #153
 Post Posted: Wed Nov 30, 2011 12:34 pm 
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Course Students


Posts: 4
The point R,T, and U lie on a circle that has a radius 4. If the length of arc RTU is 4pie/3, what is the length of line segment RU.

a) 4/3
b)8/3
c)3
d)4
e)6



I understand how to get the answer, but my confusion comes from the idea that in order for a triangle to be inscribed in a circle, the triangle needs to have a right angle. Obviously not in this case, but I'm baffled as to why (not that it takes all that much to baffle me....)
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RonPurewal
 Post subject: Re: Quant Review #153
 Post Posted: Fri Dec 09, 2011 4:43 am 
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ManhattanGMAT Staff


Posts: 7146
lsegal wrote:
my confusion comes from the idea that in order for a triangle to be inscribed in a circle, the triangle needs to have a right angle.


this is true if, and only if, the inscribed angle cuts off a semicircle (i.e., the sides of the angle hit the circle at two points that make a semicircle/diameter).

more generally, the measure of an inscribed angle is half of whatever arc it cuts off. (you can probably find a zillion illustrations of this idea, with diagrams and so on, by googling the term "inscribed angle".)
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lsegal
 Post subject: Re: Quant Review #153
 Post Posted: Mon Dec 12, 2011 2:23 pm 
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Course Students


Posts: 4
Thanks. Can't believe I didn't see that. Loving your recordings btw....
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RonPurewal
 Post subject: Re: Quant Review #153
 Post Posted: Sat Dec 24, 2011 2:54 am 
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ManhattanGMAT Staff


Posts: 7146
lsegal wrote:
Thanks. Can't believe I didn't see that. Loving your recordings btw....


thanks.
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