A rectangle is inscribed in a circle of radius r. if the width of the rectangle is x, what is the height of the rectangle?

The diagonal of length 2r forms the hypotenuse of a right angled triangle with one leg (the width of the rectangle) = x. So by Pythagoras:-

(2r) ^2 = h^2 + x^2 where h = height of the rectangle

h^2 = 4r^2 - x^2

h = √ (4r^2 - x^2) answer