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Option D: [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex]What is circle?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.A circle is also termed as the locus of the points drawn at an equidistant from the centre.What is radius?Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.What is circumference?Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.Explanation for the answer:[tex]A = \pi{({r+2})^{2}}[/tex][tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex][tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]Learn more about Circle:https://brainly.com/question/26594685#SPJ1