16. $[\mathbf{1 0}]$ Let $R$ be a semicircle with diameter $X Y$. A trapezoid $A B C D$ in which $A B$ is parallel to $C D$ is circumscribed about $R$ such that $A B$ contains $X Y$. If $A D=4, C D=5$, and $B C=6$, determine $A B$.
Answer: 10
We claim that $A B=A D+B C$. Let $O$ denote the center of $R$. Since $D A$ and $D C$ are both tangent to $R$, we have $\angle A D O=\angle O D C$. Since $C D$ is parallel to $A B$, we also have $\angle O D C=\angle D O A$. Thus $\angle A D O=\angle D O A$, and it follows that $A D=A O$. Similarly, we have $B C=B O$. Therefore, we
$$
A B=A O+B O=A D+B C=10 .
$$