1.17. One of the two parallel lines touches a circle of radius $R$ at point $A$, while the other intersects this circle at points $B$ and $C$. Express the area of triangle $A B C$ as a function of the distance $x$ between the lines.
1.17. Let the distance between the parallel lines be $x$ (Fig. 1.15); then the area $S$ of triangle $A B C$ is $0.5 B C \cdot x$. Since $O A \perp B C$, then $B M=$ $=M C$ and $B M \cdot M C=A M \cdot M D=x(2 R-$ $-x)$. Therefore, $0.25 B C^{2}=x(2 R-x)$, from which

$$
\begin{gathered}
S=0.5 x \cdot 2 \sqrt{2 R x-x^{2}}=x \sqrt{2 R x-x^{2}} . \\
\text { Answer: } S=x \sqrt{2 R x-x^{2}} .
\end{gathered}
$$