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triangle inside circle gmat prep practice test #1

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urooj.khan
 Post subject: triangle inside circle gmat prep practice test #1
 Post Posted: Sun May 31, 2009 10:49 am 
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Posts: 17
hi
i've been spending alot of time on this question and cant seem to get anywhere.. please help!

the question is
there is a triangle inside a circle...the diameter of the circle is 2 which is the base of the triangle... the centre of the circle is point O. Segment AO = OC = 1. A and C are on the very edge of the circle and are also points that make up the triangle ABC.

The length of segment BC is also = 1. Triangle ABC is not a right triangle or an isoceles triangle...

the question asks to find the area of the triangle.

if only i could figure out how to get the height of this triangle
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stock.mojo11
 Post subject: Re: triangle inside circle gmat prep practice test #1
 Post Posted: Sun May 31, 2009 5:10 pm 
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If a triangle is inscribed in a circle with diameter as one side, that triangle is a right angled triangle. The vice versa is also true.

Now you know that the triangle is right angled, you can find the area after finding AB using Pythagoras theorem
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urooj.khan
 Post subject: Re: triangle inside circle gmat prep practice test #1
 Post Posted: Sun May 31, 2009 5:20 pm 
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Posts: 17
thanks stock.mojo11 !!

gotta know these properties better!
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RonPurewal
 Post subject: Re: triangle inside circle gmat prep practice test #1
 Post Posted: Fri Jun 05, 2009 4:48 am 
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ManhattanGMAT Staff


Posts: 7146
stock.mojo11 wrote:
If a triangle is inscribed in a circle with diameter as one side, that triangle is a right angled triangle. The vice versa is also true.


this is correct.

in fact, this is not some case of special pleading for right angles. this is just one case of the more general fact that an INSCRIBED ANGLE (i.e., an angle whose vertex lies ON the circle itself, and whose sides go through the circle's interior) is equal to half the number of degrees in the arc.
since the semicircle is 180 degrees, the inscribed angle is half of 180, or 90 degrees.

of course, this case is frequent enough (i.e., it shows up more often than do other types of inscribed angles) that it may merit separate memorization.
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