Pentagon in a Circle

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


The answer is 7.

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