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2021 Team P7

Source:

March 2, 2021
geometry

Problem Statement

Let PP and QQ be fixed points in the Euclidean plane. Consider another point O0O_0. Define Oi+1O_{i+1} as the center of the unique circle passing through OiO_i, PP and QQ. (Assume that Oi,P,QO_i,P,Q are never collinear.) How many possible positions of O0O_0 satisfy that O2021=O0O_{2021}=O_{0}?
Proposed by Fei Peng
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