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5

Part of 1974 Czech and Slovak Olympiad III A

Problems(1)

Areas in cyclic hexagon

Source: Czech and Slovak Olympiad 1974, National Round, Problem 5

7/19/2024
Let ABCDEFABCDEF be a cyclic hexagon such that AB=BC,  CD=DE,  EF=FA. Show that [ACE]≤[BDF][ACE]\le[BDF] and determine when the equality holds. ([XYZ][XYZ] denotes the area of the triangle XYZ.XYZ.)
geometryGeometric Inequalitiesgeometrical inequalitiesinequalitiesCyclichexagonarea