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what is the area of the largest quadrileteral that can be inscribed in a circle with an...

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gaara1012 | Salutatorian

Posted August 26, 2013 at 7:48 AM via web

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what is the area of the largest quadrileteral that can be inscribed in a circle with an area of 64pie? 

1. 64

2. 72

3. 96

4. 108

5. 128

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted August 26, 2013 at 8:32 AM (Answer #1)

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The largest quadrilateral that can be inscribed in a circle is the square whose diagonal is the diameter of the circle.

Since the circle's area is: `A = 64pi,`

This means that `64 = r^2,`

so the radius of the circle is `8.`

Now, that makes the length of the diagonal of the square equivalent to:  `16.`

The diagonal is the hypotenuse length of a `45-45-90 triangle.`

When given the hypotenuse of this special triangle the length of the sides are:  `16 /sqrt(2)`

Simplified this gives the square a side length of `8sqrt(2).`

Since this isa square and all side lengths are equal to find area of square:  `A = s^2.`

So `A = (8sqrt(2))^2`

So the area of the square (the largest) is `128.`

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