How Can You Maximize the Area of a Triangle with Vertices on a Circle?

[Dustinsfl]

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

What is the best way to maximize the area of a triangle in this instance?

 

[LCKurtz]

Put one vertex at (1,0), the second around at angle θ, calculate the corresponding area and maximize it as a function of θ.

 

[Dustinsfl]

The area of a triangle inscribed in circle is 1/2 * (AB)^{2} * sin(theta), correct? A 90 degree angle is going to yield maximum multiple of AB; however, is a lesser or greater angle with a longer length going to increase the area more?

 

[LCKurtz]

What are A and B? The only variable in the problem is θ. And, no, that is not the correct formula for a triangle with sides A and B and included angle θ.

 

[Dustinsfl]

Then what is the formula for the area of a triangle using an angle theta?

 

[Dustinsfl]

The answer is 1/2, right?

 

[LCKurtz]

You are reviewing for the GRE and you can't figure that out?? Draw a little triangle with sides A and B, included angle θ and height h and figure out its area.