How many distinct right triangles with integer sides circumscribe a circle of radius 10?
###### This problem was inspired by the *Jiu Zhang Suan Shu*

Note: by distinct I mean we do not count any permutation of \(\left( a,b \right) \).

e.g. The Pythagorean triple (12, 5 ,13) describes the same triangle as (5, 12 ,13) .

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