In the graphic we have an isosceles triangle, and the problem is
Calculate $\text{m}\angle BCD$

I added the point $E$ at distance $x$ from $C$ because it causes $DE=x$, after playing with geogebra. With this, the question is easily solved. Of course since the triangle is determined (Since the ratios are scale invariant, we can WLOG assume $x=1$)we can prove $DE=x$ using trigonometry, but what is the elegant, geometric-like way of showing it?
