DK-GEORGMOHR 2010 Problem 4

An equilateral triangle $ABC$ is given. With $BC$ as diameter, a semicircle is drawn outside the triangle. On the semicircle, points $D$ and $E$ are chosen such that the arc lengths $BD, DE$ and $EC$ are equal. Prove that the line segments $AD$ and $AE$ divide the side $BC$ into three equal parts.