GRE Math : How to find the ratio of diameter and circumference
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Example Questions
Example Question #1211 : Gre Quantitative Reasoning
A circle with an area of 
From the ratio given 
or
The largest sector thus has an area equal to
Example Question #1212 : Gre Quantitative Reasoning
A rectangle is inscribed inside of a circle such that every corner touches the edge of the circle. If the area of the rectangle is 
The answer cannot be determined.
To find the area of the circle, it is important to know either its diameter or radius. For the geometry described in this problem, this is the same as the diagonal of the rectangle.
However, to find the diagonal of the rectangle, the sides must first be known. They can be found, since the perimeter and area are given:
This system of equation can be solved by substitution:
Followed by:
Note that this gives two possible values for 
Knowing these two values, the diagonal can be found; it is the hypotenuse of a right triangle formed by these two lengths:
Since the diagonal is also the diameter, the area of the circle is given by:
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