17. As shown in the figure, given that $P A$ is a tangent to $\odot O$, $A$ is the point of tangency, line $P O$ intersects $\odot O$ at points $B$ and $C$, $D$ is the midpoint of $O C$, and line $A D$ is extended to intersect $\odot O$ at point $E$. If $P A=2 \sqrt{3}$ and $\angle A P B=30^{\circ}$.
(1) Find the size of $\angle A E C$; (2) Find the length of $A E$.
(1) $O A \perp P A, \angle A P B=30^{\circ} \Rightarrow \angle P O A=60^{\circ}$, so $\triangle O A B$ is an equilateral triangle.

Therefore, $\angle A E C=\angle A B C=60^{\circ}$.
(2) $P A=2 \sqrt{3} \Rightarrow P O=4, O A=O B=2 \Rightarrow P D=5$.

In $\triangle P A D$, $A D^{2}=12+25-2 \cdot 2 \sqrt{3} \cdot 5 \cdot \frac{\sqrt{3}}{2}=7 \Rightarrow A D=\sqrt{7}$,
and $A D \cdot D E=B D \cdot D C \Rightarrow D E=\frac{3}{\sqrt{7}}=\frac{3 \sqrt{7}}{7} \Rightarrow A E=\frac{10 \sqrt{7}}{7}$.