Question 73
Let $A$, $B$, $C$, $D$ (written in the order from left to right) be four equally-spaced collinear points. Let $\omega$ and $\omega'$ be the circles with diameters $AD$ and $BD$, respectively. A line through $A$ that is tangent to $\omega'$ intersects $\omega$ again at point $E$. If $AB = 2\sqrt{3}\ \mathrm{cm}$, what is $AE$?