PS

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.