Passel Of Techniques

Geometry Level 4

ABCABC is a right triangle with B=90\angle B= 90^\circ.
EE and FF are the mid-points of ABAB and ACAC, respectively.
The incenter II of triangle ABCABC lies on the circumcircle of triangle AEFAEF,

Find the ratio BCAB \dfrac{BC}{AB} .

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

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