Angle Chasing

Geometry Level 5

Let $$ABC$$ be an acute-angled triangle, and let $$D,E,F$$ be points on $$BC, CA,AB$$ respectively such that $$AD$$ is the median, $$B$$E is the internal angle bisector and $$CF$$ is the altitude. Suppose $$\angle FDE= \angle ACB , \angle DEF=\angle BAC$$ and $$\angle EFD =\angle ABC$$. If $$\angle BAC +\angle ABC= \alpha$$ , submit your answer as sum of all positive integer divisors of $$\alpha$$.

×