What is the greatest possible area of a triangle region with

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imane81: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Wed Jan 13, 2010 7:17 pmFollowed by: 1 member; Thanked: 1 times

by imane81 » Thu Feb 18, 2010 12:21 pm

Please advise on this one

What is the greatest possible area of a triangle region with one vertex at the center of a circle of radius 1 and the other 2 vertices on the circle?
A. sqrt(3)/4
B. 1/2
C. pi/4
D. 1
E. sqrt(2)

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Source: Beat The GMAT — Problem Solving | Thu Feb 18, 2010 12:21 pm

Osirus@VeritasPrep: GMAT Instructor; Posts: 1578; Joined: Thu May 28, 2009 8:02 amFollowed by: 34 members; Thanked: 128 times; GMAT Score:760

by Osirus@VeritasPrep » Thu Feb 18, 2010 12:25 pm

I would pick B

To find the greatest area we want to maximize the base and the height. If one vertex is at the center and the other two points lie on the circle, that means that two sides have length 1. Which means that the triangle is at the least an isoceles triangle. the two legs would be 1 and 1. The area would be .5bh or in this case .5(1)(1)= 1/2

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu Feb 18, 2010 12:53 pm

imane81 wrote:Please advise on this one

What is the greatest possible area of a triangle region with one vertex at the center of a circle of radius 1 and the other 2 vertices on the circle?
A. sqrt(3)/4
B. 1/2
C. pi/4
D. 1
E. sqrt(2)

If the triangle makes 90 degrees at the center the area = 1/2
If the triangle makes 60 degrees at the center the area = sqrt(3)/4
If the triangle makes 120 degrees at the center the area = sqrt(3)/4

I go for B

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