It doesn't have to be regular!

Geometry Level pending

A hexagon is inscribed in a circle of radius \(r\). Two of its sides have length 1, two of them have length 2, two of them have length 3. If \(r\) is a root of \(ax^{3}+bx^{2}+cx+d=0\), where \(|a|, |c|\) and \(|d|\) are prime numbers, then find the value of \(|a|+|b|+|c|+|d|\).


This is a problem found in most math books for IIT JEE.
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