# Simplicity is the most complex thing . Part 3

Geometry Level 5

$$ABC$$ is a triangle in which $$AD$$ is the bisector of angle $$A$$ such that $$\angle ADB = 120 ^\circ$$. $$AB : AC = 3 :1$$ and $$AD = 10 \text{ cm}$$. $$CE$$ is the median on side $$AB$$ of triangle $$ABC$$. $$O$$ is the centroid of the triangle $$ABC$$. Through $$O$$ a line $$OF \parallel EA$$ is drawn. Find the area of triangle $$OFC$$ in $$\text{cm}^2$$.