# 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 \(|a|+|b|+|c|+|d|\).