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Romania NMO 2023 Grade 6 P4

Source: Romania National Olympiad 2023

April 14, 2023
geometryangles

Problem Statement

Let ABCABC be a triangle with ∠BAC=90∘\angle BAC = 90^{\circ} and ∠ACB=54∘.\angle ACB = 54^{\circ}. We construct bisector BD(D∈AC)BD (D \in AC) of angle ABCABC and consider point E∈(BD)E \in (BD) such that DE=DC.DE = DC. Show that BE=2⋅AD.BE = 2 \cdot AD.
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