The maximum area of the triangle formed by the circle $x^2+y^2=a^2$ with two of its vertices are diametrically opposite points is?

Question

$\begin{array}{1 1}(a)\;a^2\\(b)\;\large\frac{a^2}{2}\\(c)\;\large\frac{a^2}{4}\\(d)\;\text{none of these}\end{array}$