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Geometric inequality

Source: Saint Petersburg MO 2020 Grade 9 Problem 3 & Grade 10 Problem 3

May 7, 2020
geometric inequalityinequalities

Problem Statement

On the side ADAD of the convex quadrilateral ABCDABCD with an acute angle at BB, a point EE is marked. It is known that ∠CAD=∠ADC=∠ABE=∠DBE\angle CAD = \angle ADC=\angle ABE =\angle DBE. (Grade 9 version) Prove that BE+CE<ADBE+CE<AD. (Grade 10 version) Prove that △BCE\triangle BCE is isosceles.(Here the condition that ∠B\angle B is acute is not necessary.)
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