Circle-ception

Geometry Level 3

A quadrant of a circle of radius \(10\) has a circle inscribed in it - its diameter can be written as \(a\left( \sqrt { b } -c \right) \) in fully factorised form, where \(b\) is square free and \(a\), \(b\) and \(c\) are integers.

Find the value of\[\large\left\lfloor \frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 } }{ a+b+c } \right\rfloor. \]

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