G1.1 In Figure $1, B C$ is the diameter of the circle. $A$ is a point on the circle, $A B$ and $A C$ are line segments and $A D$ is a line segment perpendicular to $B C$. If $B D=1, D C=4$ and $A D=a$, find the value of $a$.
$\begin{array}{l}\triangle A B D \sim \triangle C A D \text { (equiangular) } \\ \frac{a}{1}=\frac{4}{a} \text { (ratio of sides } \sim \Delta \text { 's) } \\ a^{2}=1 \times 4 \\ a=2\end{array}$