# Just another provocative triangle

**Geometry**Level 3

Consider a triangle **ABC** with **AB=3**, **BC=6**, **CA=5**. Let the angle bisector of angle **BAC** intersect side **BC** at a point **D** and **E** is the middle of the segment **BD**. If **I** is the incenter of the triangle **ABC** and **F∈(AC)** with **FC=k FA** , find the INTEGER value of **k** so that **E,I,F** are collinear.
**[k]=?**

I.E. The integer value of 25.623=[25.623]=25 ; [0.124]=0 .