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danjuma: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Thu Aug 26, 2010 9:29 am; Thanked: 4 times

by danjuma » Mon Nov 01, 2010 8:54 pm

What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other 2 vertices on the circle?

1. 1

2.1/2

3. 1/4

4. 1/3

5. 2

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Source: Beat The GMAT — Problem Solving | Mon Nov 01, 2010 8:54 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Nov 01, 2010 10:00 pm

danjuma wrote:What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other 2 vertices on the circle?

1. 1
2.1/2
3. 1/4
4. 1/3
5. 2

When two sides of a triangle is given, then we will get the largest area by making the angle between them a right angle. This is because,

Area of triangle = (Product of two sides)*(Sine of angle between them)/2

Now, if two sides of a triangle are given, then area is proportional to the sine of angle between them. To maximize area, we have to maximize the sine of the angle between them. Sine of a angle is maximum for the angle = 90Â°.

In this question, two sides of the triangle is also the radius off the circle.
Thus, greatest possible area = (1)*(1)/2 = 1/2

The correct answer is B.

Rahul Lakhani
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Gurome, Inc.
https://www.GuroMe.com
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