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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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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 = 90°.

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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