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hexagon with sides 1,1,2,2,3,3 find it's circumradius

Source: Nordic Mathematical Contest 1993 #2 also 2018 Iberoamerican Shortlist G1

October 5, 2017
hexagoncircumcirclegeometry

Problem Statement

A hexagon is inscribed in a circle of radius rr. Two of the sides of the hexagon have length 11, two have length 22 and two have length 33. Show that rr satisfies the equation 2r3−7r−3=02r^3 - 7r - 3 = 0.
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