Question

Let \(P_0\) be a point outside an equilateral triangle \(A B C\) such that \(A P_0 C\) is an isosceles triangle with a right angle at \(P_0\). A grasshopper starts at \(P_0\) and turns around the triangle as follows. From \(P_0\), the grasshopper jumps to the point \(P_1\) symmetric to \(P_0\) with respect to \(A\); then it jumps to the point \(P_2\) symmetric to \(P_1\) with respect to \(B\), then to the point \(P_3\) symmetric to \(P_2\) with respect to \(C\), etc. For each \(n \in \mathbb{N}\), compare the distances \(P_0 P_1\) and \(P_0 P_n\).