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maximum length in a equilateral, on 2 concentric circles

Source: JBMO Shortlist 2005

January 1, 2018

geometrymaximumconcentricEquilateral Triangle

Problem Statement

Let

O

be the center of the concentric circles

C_1,C_2

of radii

3

and

5

respectively. Let

A\in C_1, B\in C_2

and

C

point so that triangle

ABC

is equilateral. Find the maximum length of

[OC]