PAMO 2001 Problem 3

Let $ABC$ be an equilateral triangle and let $P_0$ be a point outside this triangle, such that $\triangle{AP_0C}$ is an isoscele triangle with a right angle at $P_0$ . A grasshopper starts from $P_0$ and turns around the triangle as follows. From $P_0$ the grasshopper jumps to $P_1$ , which is the symmetric point of $P_0$ with respect to $A$ . From $P_1$ , the grasshopper jumps to $P_2$ , which is the symmetric point of $P_1$ with respect to $B$ . Then the grasshopper jumps to $P_3$ which is the symmetric point of $P_2$ with respect to $C$ , and so on. Compare the distance $P_0P_1$ and $P_0P_n$ . $n \in N$ .