Example 1. Draw a tangent line to the circle $x^{2}+y^{2}=25$ through point C $(6,-8)$, find the distance from C to the line connecting the two points of tangency.

保留了原文的格式和换行。
Solve: As shown in Figure 2, the equation of the chord of contact A.B is:
$$
6 x-8 y-25=0 \text {. }
$$

The distance from C $(6,-8)$ to the chord of contact $\mathrm{AB}$ is:
$$
\mathrm{d}=\frac{|36+64-25|}{\sqrt{6^{2}+(-8)^{2}}}=7.5 .
$$