Pentagon in a Circle

Level pending

Regular pentagon \(ABCDE\) is inscribed inside a circle. A point \(P\) is picked on an arc on the circle strictly between \(A\) and \(E\). If \(\dfrac{PA+PB+PD+PE}{PC}\) can be expressed as \(\dfrac{a\sqrt{b}}{c}\) where \(a,c\) are relatively prime positive integers and \(b\) is a positive integer not divisible by a perfect square, then find \(a+b+c\).

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