Problem

Source: Iranian National Olympiad (3rd Round) 2003

Tags: geometry proposed, geometry



Segment $ AB$ is fixed in plane. Find the largest $ n$, such that there are $ n$ points $ P_1,P_2,\dots,P_n$ in plane that triangles $ ABP_i$ are similar for $ 1\leq i\leq n$. Prove that all of $ P_i$'s lie on a circle.