# Dilated Steiner Inellipse

Geometry Level 5

Triangle has vertices $$A=(0,0), B=(9,0), C=(3,6)$$. Its Steiner inellipse is dilated from triangle centroid. New ellipse trisects all three sides of the triangle $$ABC$$.

Given that the dilation factor can be expressed as $$\dfrac{a}{\sqrt{b}}$$, where $$a$$ and $$b$$ are positive integers with $$b$$ square-free.

Find $$a+b$$.

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