The area of an ellipse is twice that of a circle. The major diameter of the ellipse is twice that of the minor diameter. The radius of the circle is

Let the semi-major and semi-minor axes be a and b. The area of an ellipse is πab. Major diameter = 2a and minor diameter = 2b; given major diameter is twice the minor diameter, so 2a = 2·(2b) ⇒ a = 2b. The circle’s area is πr^2, so “ellipse area = twice circle area” gives πab = 2·πr^2. Using a = 2b, π(2b)b = 2·πr^2 ⇒ 2b^2 = 2r^2 ⇒ r = b. Thus the circle’s radius equals the semi-minor axis b, which is half the minor diameter (minor diameter = 2b). This means the radius is 50% of the ellipse’s minor diameter.