A cyclic quadrilateral $ABCD$ has side lengths $AB = 3, BC = AD = 5$, and $CD = 8$. The radius of its circumcircle can be written in the form $a\sqrt{b}/c$, where $a, b, c$ are positive integers, $a, c$ are relatively prime, and $b$ is not divisible by the square of any prime. Find $a + b + c$.


Let's think step by step and output the final answer within \boxed{}.
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