2000 Fermat Problem 19

An ant walks inside a 18\,\text{cm} by 150\,\text{cm} rectangle. The ant's path follows straight lines which always make angles of 45^\circ to the sides of the rectangle. The ant starts from a point X on one of the shorter sides. The first time the ant reaches the opposite side, it arrives at the mid-point. What is the distance, in centimetres, from X to the nearest corner of the rectangle?

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 8\quad \textbf{(E)}\ 9

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