$\overline{AB}$ is a diameter of a circle. Tangents $\overline{AD}$ and $\overline{BC}$ are drawn so that $\overline{AC}$ and $\overline{BD}$ intersect in a point on the circle. If $\overline{AD}=a$ and $\overline{BC}=b$, $a \not= b$, the diameter of the circle is:
$\textbf{(A)}\ |a-b|$$\textbf{(B)}\ \frac{1}{2}(a+b)$$\textbf{(C)}\ \sqrt{ab}$$\textbf{(D)}\ \frac{ab}{a+b}$$\textbf{(E)}\ \frac{1}{2}\frac{ab}{a+b}$