tmua.me Extreme Set A Paper 1 · Question 17

A particle starts at the centre $P$ of a rectangle with side lengths $3$ and $2$ . It moves in straight lines inside the rectangle. Whenever it reaches a side, it is reflected so that the incoming and outgoing segments make equal angles with that side. Its path never passes through a vertex.

The particle returns to $P$ for the first time after exactly $15$ reflections.

What is the least possible total distance travelled before this first return?

\dfrac{90}{\sqrt{13}}

25

2\sqrt{157}

\sqrt{697}

4\sqrt{157}

\text{Such a path is impossible}

examday

tmua.me Extreme Set A Paper 1 · Q17