Consider the isosceles triangle $ABC$ inscribed in the semicircle of radius $ r$. If the $\vartriangle BCD$ and $\vartriangle CAE$ are equilateral, determine the altitude of $\vartriangle DEC$ on the side $DE$ in terms of $ r$.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2014 3.4
Tags: semicircle, equilaterals, isosceles, geometry
