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2022 Polish Junior Math Olympiad Second Round P4

Source: 2022 Polish Junior Math Olympiad Second Round

May 21, 2023
geometry

Problem Statement

In the convex pentagon ABCDEABCDE, the following equalities hold: ∠CDE=90∘\angle CDE=90^\circ, AC=ADAC=AD, and BD=BEBD=BE. Prove that triangle ABDABD and quadrilateral ABCEABCE have the same area.
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