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 $$p+q$$.

×