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

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In summary, the conversation discusses finding the greatest possible area of a triangular region with one vertex at the center of a circle with radius 1 and the other two vertices on the circle. The best way to maximize the area is to put one vertex at (1,0), the second at an angle θ, and calculate the corresponding area. The formula for the area of a triangle inscribed in a circle is 1/2 * (AB)^2 * sin(θ), where A and B are the sides of the triangle. It is mentioned that a 90 degree angle will yield the maximum area, but it is questioned whether a lesser or greater angle with a longer length will increase the area more. The correct formula for the area
  • #1
Dustinsfl
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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?
 
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  • #2
Put one vertex at (1,0), the second around at angle θ, calculate the corresponding area and maximize it as a function of θ.
 
  • #3
The area of a triangle inscribed in circle is 1/2 * (AB)[tex]^{2}[/tex] * 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?
 
  • #4
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.
 
  • #5
Then what is the formula for the area of a triangle using an angle theta?
 
  • #6
The answer is 1/2, right?
 
  • #7
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.
 

1. What is the format of the GRE?

The GRE consists of three sections - verbal reasoning, quantitative reasoning, and analytical writing. The verbal and quantitative reasoning sections are multiple-choice, while the analytical writing section requires you to write essays.

2. How many times can I take the GRE?

You can take the GRE once every 21 days, up to five times within any continuous 12-month period. However, most graduate programs only consider your highest score.

3. How long is the GRE?

The total testing time for the GRE is approximately 3 hours and 45 minutes, including breaks. The verbal reasoning and quantitative reasoning sections are each 1 hour and 10 minutes, and the analytical writing section is 1 hour.

4. Can I use a calculator on the GRE?

Yes, you can use a calculator on the quantitative reasoning section. However, it is a basic on-screen calculator that you cannot bring in yourself. You are not allowed to use a calculator on the verbal reasoning section.

5. How is the GRE scored?

The verbal reasoning and quantitative reasoning sections are scored on a scale of 130-170, and the analytical writing section is scored on a scale of 0-6. Your total score is the sum of your scores on the verbal and quantitative reasoning sections.

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