BMT 2022 Geometry #8
Source:
August 12, 2023
geometry
Problem Statement
Anton is playing a game with shapes. He starts with a circle of radius , and to get a new circle , he circumscribes a square about and then circumscribes circle about that square. To get another new circle , he circumscribes a regular octagon about circle and then circumscribes circle about that octagon. He continues like this, circumscribing a -gon about and then circumscribing a new circle about the -gon. As increases, the area of approaches a constant . Compute .