A geometry problem by Brilliant Member

Geometry Level 3

Let \(m^2\) be a constant real number such that \(x+y=1\) is tangent to the curve \(x^2 + y^2 =m^2\).

If the value of \(m^2\) can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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