Another GRE questions

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  • #1
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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
LCKurtz
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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
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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
LCKurtz
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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
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Then what is the formula for the area of a triangle using an angle theta?
 
  • #6
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The answer is 1/2, right?
 
  • #7
LCKurtz
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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.
 

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