Find the circumference of the given circle with the inscribed square - which contains sides 6 cm in length.
A) 3 • sq root of 2 • pi cm
B) 6 • sq root of 2 • pi cm
C) 12 pi cm
D) 5 pi cm
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Step-by-step explanation:
Let ABCD be a square inscribed in a circle of radius 'r'. Now, the diameter of circle is the diagonal of square.
Therefore, BD=2r. In △BDC, using Pythagoras theorem
BC2+CD2=BD2⇒a2+a2=(2r)2⇒2a2=4r2⇒a2=2r2
∴Area of square=2r2
Area of circle=πr2
Required ration=πr2:2r2=π:2
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