The angle $\angle XOY =\alpha $ and the points $A$ and $B$ on OY are given such that $OA = a$ and $OB = b$ with $a > b$. A circle passes through the points $A$ and $B$ and is tangent to $OX$. a) Calculate the radius of that circle in terms of $a, b$ and $\alpha $. b) If $a$ and $b$ are constants and $\alpha $ varies, show that the minimum value of the radius of the circle is $\frac{a-b}{2}$.