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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