\textbf{36.} Line $d$ has equation $y - x = 0$. A circle with center at the origin has a radius twice that of another circle. If line $d$ is tangent to the smaller circle with equation $x^2 + y^2 + 6x - 2y = r$, what is the product of the lengths of the chord(s) of intersection of the two circles?
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(1) $\dfrac{5}{2}$ \hspace{1cm} (2) $\dfrac{5}{4}$ \hspace{1cm} (3) $\dfrac{65}{32}$ \hspace{1cm} (4) $\dfrac{65}{64}$
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