A geometry problem by kshetrapal dashottar

Geometry Level 4

Let $$ABC$$ be a right triangle with $$\angle B = 90^\circ$$. Let $$E$$ and $$F$$ be the mid-points of $$AB$$ and $$AC$$, respectively . Suppose the incenter $$I$$ of triangle $$ABC$$ lies on the circumcircle of triangle $$AEF$$. Find the ratio $$\dfrac{BC}{AB}$$.

Give your answer to 2 decimal places.

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