# Mirror, Mirror

Geometry Level 5

The minimum possible perimeter of a triangle with one vertex at $$(3,9)$$, one anywhere on the $$y$$-axis and one anywhere on the line $$y = x$$ is $$a\sqrt{b}$$, where $$a$$ and $$b$$ are positive coprime integers and $$b$$ is square free. Find $$a + b.$$

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