# 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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