Problem - 2512
There are several equally spaced parallel lines on a table. The distance between two adjacent lines is $2a$. On the table, toss a coin with a radius of $r$, $(r < a)$. Find the probability that the coin does not touch any line.
This is a typical geometric probability problem. The answer is $\boxed{\frac{a-r}{r}}$. It is clear from the diagram below that the coin will not touch the lines if and only if its center falls within the two dashed lines.
