What is the perimeter of a square inscribed in a circle with a radius of 12 units?

1 Answer
CW
May 12, 2017

perimeter #=48sqrt2# units

Explanation:

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When a square is inscribed in a circle, the diagonal of the square equals the diameter of the circle.

As shown in the figure, #BD=2*r#
where #BD# is the diagonal of the square and #r# is the radius of the circle.
#DeltaABD# is a right isosceles triangle with hypotenuse #(BD)# and two equal legs #(a)#.

By Pythagorean theorem,
#BD^2=a^2+a^2#
Given #r=12#,
#=> (2xx12)^2=2a^2#
#=> 576=2a^2#
#=> a^2=576/2=288#
#=> a=sqrt288=sqrt(144xx2)=12sqrt2#
Perimeter of the square #=4a=4xx12sqrt2=48sqrt2# units

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