How can I find the smallest enclosing circle for a rectangle?

Question

I have the four vertices of a rectangle. I need to find it's smallest enclosing circle. For example:

I need to find the radius of the circle.

Answer 1

Take half of the distance between the endpoints of a diagonal of the rectangle.

Answer 2

There is only one such circle for a rectangle. If your rectangle has sidelengths $a$ and $b$, then the length of the diagonal (by the Pythagorean theorem) is $\sqrt{a^2+b^2}$. Since the diagonal is a diameter, the radius is just $\dfrac{\sqrt{a^2+b^2}}{2}$.

Answer 3

While pythagorean theorum works well for enclosing a square with a circle and predicting the diameter, I am concerned that it does not work for a rectangle where the hypotenuse is not perpendicular to the tangent of the circle at its end points. Is this a valid concern?