# Inspired By Brian Charlesworth!

Let $$S$$ be the set of all distinct Pythagorean Triplets $$(a,b,c)$$ where $$a,b,c$$ are positive integers and $$a<b<c$$ such that $$ab=10(a+b+c)$$.

Let the sum of all distinct values of $$c$$ of the elements of $$S$$ be $$x$$.

Let the number of elements or Pythagorean Triplets present in the set $$S$$ be $$y$$.

Let the sum of all distinct Inradii of all such Right Angled Triangles formed by the Pythagorean Triplets present in $$S$$ be $$z$$.

Find the value of $$x+y+z$$.

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