MathNet 1968 — Part 01 Question 5

Given a triangle $ABC$, and $D$ on the segment $AB$, $E$ on the segment $AC$, such that $AD = DE = AC$, $BD = AE$, and $DE$ is parallel to $BC$. Prove that $BD$ equals the side of a regular 10-gon inscribed in a circle with radius $AC$.