Find the radius of a circle that circumscribes a square whose perimeter is 25 inches?

Find the radius of a circle that circumscribes a square whose perimeter is 25 inches.

1 Answer
Abhishek K.
Apr 12, 2018

radius#=(3.125*sqrt2)# inches

Explanation:

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#rarr#perimeter of square ABCD#=25#

#rarr4AB=25#

#rarrAB=6.25#

Now in rt #DeltaABD#,

#rarrAD^2=AB^2+BD^2=AB^2+AB^2=2AB^2#

#rarrAD=sqrt2*AB=6.25sqrt2#

AD is the the diameter of the circle as inscribed angle on circumference is a right angle.

So, radius#=(AD)/2=6.25**sqrt2/2=3.125*sqrt2#

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