9. As shown in the figure, $AB$ is the diameter of the unit circle. Take any point $D$ on $AB$, and construct $DC \perp AB$, intersecting the circumference at $C$. If the coordinates of point $D$ are $(x, 0)$, then when $x \in$ $\qquad$, segments $AD$, $BD$, and $CD$ can form an acute triangle.
According to the problem, $A D=1+x, B D=1-x, C D=\sqrt{1-x^{2}}$, since $A D, C D, B D$ form a geometric sequence, thus $\left\{\begin{array}{l}(1-x)^{2}+1-x^{2}>(1+x)^{2}, \\ (1+x)^{2}+1-x^{2}>(1-x)^{2}\end{array} \Rightarrow\left\{\begin{array}{l}x^{2}+4 x-1<0, \\ x^{2}-4 x-1<0\end{array}\right.\right.$ $\Rightarrow 2-\sqrt{5}<x<\sqrt{5}-2$. Therefore, $x \in(2-\sqrt{5}, \sqrt{5}-2)$. Solution