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Points lie on a circle

Source: Iranian National Olympiad (3rd Round) 2003

January 24, 2009
geometry proposedgeometry

Problem Statement

Segment AB AB is fixed in plane. Find the largest n n, such that there are n n points P1,P2,…,Pn P_1,P_2,\dots,P_n in plane that triangles ABPi ABP_i are similar for 1≤i≤n 1\leq i\leq n. Prove that all of Pi P_i's lie on a circle.
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