1. (2000 Hebei Province Competition Question) In the circle $x^{2}+y^{2}-5 x=0$, there are three chords passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$ whose lengths form a geometric sequence. Then the range of the common ratio is ( ).
A. $\left[\frac{\sqrt{2}}{\sqrt[4]{5}}, \frac{2}{\sqrt{5}}\right]$
B. $\left[\sqrt[3]{\frac{4}{5}}, \frac{2}{\sqrt{5}}\right]$
C. $\left[\frac{2}{\sqrt{5}}, \frac{\sqrt{5}}{2}\right]$
D. $\left[\frac{2}{\sqrt[3]{5}}, \frac{\sqrt{5}}{2}\right]$
1. Choose C. Reason: It is easy to obtain that the diameter of the circle $x^{2}+y^{2}-5 x=0$ is 5, so the maximum length of the chord passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$ is 5. Also, the chord passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$ and perpendicular to the diameter through that point is the shortest, with a length of 4. From $a_{3}=a_{1} q^{2}$