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Determine if there exists a convex hexagon $ABCDEF$ with

Source: Caucasus MO 2023

July 16, 2023
geometry

Problem Statement

a) Determine if there exists a convex hexagon ABCDEFABCDEF with ∠ABD+∠AED>180∘,\angle ABD + \angle AED > 180^{\circ}, ∠BCE+∠BFE>180∘,\angle BCE + \angle BFE > 180^{\circ}, ∠CDF+∠CAF>180∘.\angle CDF + \angle CAF > 180^{\circ}. b) The same question, with additional condition, that diagonals AD,BE,AD, BE, and CFCF are concurrent.
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