Question 7
Let $\triangle ABC$ be an acute-angled triangle and let $BCD$, $ACE$ and $ABF$ be equilateral triangles drawn on the outside of triangle $ABC$. Let $M$ be the midpoint of the segment $\overline{BD}$, and let $O$ be the centre of the triangle $ACE$. Prove that $|AM| : |OF| = \frac{\sqrt{3}}{2}$.