Problem

Source: Polish Junior Math Olympiad 2019 Finals

Tags: geometry, geometrical intequalities, geometric inequality, inequalities



The point $D$ lies on the side $AB$ of the triangle $ABC$. Assume that there exists such a point $E$ on the side $CD$, that $$ \sphericalangle EAD = \sphericalangle AED \quad \text{and} \quad \sphericalangle ECB = \sphericalangle CEB. $$Show that $AC + BC > AB + CE$.