find the equation of the circle circumscribed a square of side a
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When a square is circumscribed by a circle , the diagonal of the square is equal to thediameter of the circle.
The diagonal of the square is 33 inches.
We know from the Pythagorean Theorem that the diagonal of a square is 2√2 times the length of a side.
Therefore:
s2√=3s=32√=32√2 in.s2=3s=32=322 in.
First, find the diagonal of the square. Its length is 2√2 times the length of the side, or52√52 cm.
This value is also the diameter of the circle. So, the radius of the circle is half that length, or 52√2522 .
To find the area of the circle, use the formulaA=πr2A=πr2 .
A=π(52√2)2=π(25⋅24)=252π cm2
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