7. A chord of length $10 \mathrm{~cm}$ is drawn in a circle. Through one of its ends, a tangent to the circle is drawn, and through the other end, a secant parallel to the tangent is drawn. The inner segment of the secant is 12 cm. Find the radius of the circle.
Solution: $\quad A B=10, \quad \sqrt{r^{2}}=\sqrt{O D^{2}+B D^{2}}=\sqrt{x^{2}+6^{2}}, \quad \triangle D O B$ $B C=12,(r+x)^{2}+6^{2}=10^{2}$,
$r=? \quad(\triangle A D B)$$\Rightarrow\left\{\begin{array}{l}r+x=\sqrt{64}=8, \\ r^{2}-x^{2}=36,\end{array}\right.$,

$x=8-r, \quad r^{2}-(8-r)^{2}=36, \quad r^{2}-64+16 r-r^{2}=36, \quad 16 r=100$, $r=\frac{100}{16}=\frac{25}{4}$

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