MathNet 2012 Question 68

The two equilateral triangles $ABC$ and $ADB$ (with $C \neq D$) share the common side $AB$. The midpoints of $AC$ and $BC$ are denoted by $E$ and $F$, respectively. Show that $DE$ and $DF$ divide $AB$ into three parts of equal length.

G. Kirchner, Innsbruck



Figure 1: Problem 4.