Question 21A circle of radius $r$ passes through both foci of, and exactly four points on, the ellipse with equation $x^2 + 16y^2 = 16.$ The set of all possible values of $r$ is an interval $[a, b).$ What is $a + b?$$5\sqrt{2} + 4$$\sqrt{17} + 7$$6\sqrt{2} + 3$$\sqrt{15} + 8$$12$