# INMO-Problem-2!

Geometry Level 3

Let $$ABC$$ be an acute angled triangle in which $$D,E$$ and $$F$$ are points on $$BC,CA, AB$$ respectively such that $$AD$$ is perpendicular to $$BC,AE=EC$$ and $$CF$$ bisects $$\angle C$$ internally. Suppose $$CF$$ meets $$AD$$ and $$DE$$ in $$M$$ and $$N$$ respectively. If $$FM=2,MN=1,NC=3,$$find the perimeter of the triangle $$ABC$$.