7. As shown in Figure 2, a right-angle ruler $A B C$ is tangent to $\odot O$ at point $D$, and $A$ touches $\odot O$ at point $A$. It is measured that $A B=a, B D=b$. Then the radius of $\odot O$ is $\qquad$.
7. $\frac{a^{2}+b^{2}}{2 a}$