Circle-ception

Geometry Level 2

A quadrant of a circle of radius 1010 has a circle inscribed in it - its diameter can be written as a(bc)a\left( \sqrt { b } -c \right) in fully factorised form, where bb is square free and aa, bb and cc are integers.

Find the value ofa2b2c2a+b+c.\large\left\lfloor \frac { { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 } }{ a+b+c } \right\rfloor.

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