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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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