S.T a rectangle of maximum perimeter which can be inscribed in a circle of radius r is a square of side root2*r?

Dear Linta

let the side of rectangle is a and b and its center coinside with the center of circle.

a/2 = r cosΘ  then  b/2 =r sinΘ

now perimeter P =2a+2b

                        =4r(cosΘ + sinΘ)

                         = 4r√2sin(Θ +45)

so for maximum P   , sin(Θ +45) =1

              so Θ =45

  so a=b = r√2

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