KöMaL 2019 B5001

The base of an isosceles triangle is $a$, its apex angle is smaller than $120^{\circ}$, and the altitude drawn to the base is $m$. Each vertex of the triangle is reflected in the line of the opposite side. The three reflections form a new isosceles triangle, with a base $a'$ and an altitude $m'$ drawn to the base. Show that $\frac{a'}{a}+\frac{m'}{m}=4.$