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Areas in cyclic hexagon

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

July 19, 2024
geometryGeometric Inequalitiesgeometrical inequalitiesinequalitiesCyclichexagonarea

Problem Statement

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.)
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