Circles and Triangles

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mdavis: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Thu Nov 20, 2008 2:18 pm; Thanked: 1 times

by mdavis » Mon Feb 16, 2009 1:24 pm

In the figure above, the radius of the circle with center O is 1 and BC=1. What is the area of triangular region ABC?

sqrt2/2

sqrt3/2

1

sqrt2

sqrt3

The answer is B. I do not know how to post a figure from the GMAT prep, but the figure consists of a circle with a triangle in it. Line AC is the diameter. Would anyone be able to show me how to solve this without the picture?

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Source: Beat The GMAT — Problem Solving | Mon Feb 16, 2009 1:24 pm

Bidisha_800: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Feb 15, 2009 7:37 pmFollowed by: 1 member; Thanked: 3 times

by Bidisha_800 » Mon Feb 16, 2009 1:44 pm

Triangle ABC is right triangle with AC=2 and BC =1 so AB=sqrt(3)

area =1/2 * AB* BC = sqrt(3)/2

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fleckre: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 07, 2010 8:32 am

by fleckre » Mon Jun 14, 2010 10:00 am

How do you know triangle ABC is a right triangle?

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Mon Jun 14, 2010 10:34 am

this is becasue there is a std theorem

"states that if A is any point of the circle with diameter BC (except B or C themselves) â–³ABC is a right triangle with A the right angle. The converse states that if a right triangle is inscribed in a circle then the hypotenuse will be a diameter of the circle"

fleckre wrote:How do you know triangle ABC is a right triangle?

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fleckre: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 07, 2010 8:32 am

by fleckre » Mon Jun 14, 2010 10:46 am

Thanks - I got this question on my GMAT Prep practice test, but have yet to get to my geometry book from MGMAT. I suppose they'll cover this, but it was bothering me. Thanks again!

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luiscarlos59: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Sun Mar 13, 2011 12:34 pm; Thanked: 1 times

by luiscarlos59 » Tue Mar 22, 2011 7:23 pm

how do you know this is a right trianlge if there is no "little box" identifying the 90Â° angle?
Or do you have to assume?

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