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Beautiful geometric inequality

Source: Polish Junior Math Olympiad 2019 Finals

October 23, 2020
geometrygeometrical intequalitiesgeometric inequalityinequalities

Problem Statement

The point DD lies on the side ABAB of the triangle ABCABC. Assume that there exists such a point EE on the side CDCD, that \sphericalangle EAD = \sphericalangle AED   \text{and}   \sphericalangle ECB = \sphericalangle CEB. Show that AC+BC>AB+CEAC + BC > AB + CE.
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