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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