KöMaL 2012 K323

The apex angle of the isosceles triangle ABC is $120^o$, and the midpoint of base $AB$ is $F$. The angle bisector of $\angle$ ACF intersects base $AB$ at point $H$. $a$) Prove that $AH$=$CH$. $b$) Prove that $AH$ is one-third of the line segment $AB$.