Passel Of Techniques

Geometry Level 4

\(ABC \) is a right triangle with \(\angle B= 90^\circ\).
\(E\) and \(F\) are the mid-points of \(AB\) and \(AC\), respectively.
The incenter \(I\) of triangle \(ABC\) lies on the circumcircle of triangle \(AEF\),

Find the ratio \( \dfrac{BC}{AB} \).

If this ratio can be expressed as \( \dfrac pq\), where \(p\) and \(q\) are coprime positive integers, submit your answer as \(p+q\).

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